maximum marks total duration maximum time for … · 2016. 3. 7. · 04-03-2016 physics 15 2.00 pm...

15

COMPETITIVE EXAMINATION - 2016

DATE SUBJECT SUBJECT CODE TIME

04-03-2016 PHYSICS 15 200 pm to 500 pm

MAXIMUM MARKS TOTAL DURATION MAXIMUM TIME FOR ANSWERING

200 210 Minutes 180 Minutes

MENTION YOUR REGISTER NUMBER QUESTION BOOKLET DETAILS

QUESTION BOOKLET SERIAL NO amp VERSION NO

DOs

1 Check whether the Register No has been entered and shaded in the respective circles on the OMR answer sheet

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3 Check whether the subject name has been written and the subject code has been entered and shaded in the respective circles on the OMR answer sheet

4 This question booklet will be issued to you by the invigilator after the 2nd

bell ie after 155 pm 5 The serial number of this question booklet should be entered on the OMR answer sheet 6 The Version Number of this question booklet should be entered on the OMR answer sheet and the respective

circles should also be shaded completely 7 Compulsorily sign at the bottom portion of the OMR answer sheet in the space provided

DONTs

1 The timing and markrsquos printed on the OMR answer sheet should not be damaged mutilated spoiled 2 The 3

rd Bell rings at 200 pm till then

bull Do not remove the seal on the right hand side of this question booklet bull Do not look inside this question booklet bull Do not start answering on the OMR answer sheet

IMPORTANT INSTRUCTIONS TO CANDIDATES

1 This question booklet contains 100 questions and each question will have one statement and four distracters (Four different options choices)

2 After the 3rd

Bell is rung at 200 pm remove the seal on the right hand side of this question booklet and check that this booklet does not have any unprinted or torn or missing pages or items etc if so get it replaced by complete test booklet Read each item and start answering on the OMR answer sheet

3 During the subsequent 180 minutes bull Read each question carefully bull Choose the correct answer from out of the four available distracters (options choices) given under each

question statement bull Completely darken shade the relevant circle with a blue or black ink ballpoint pen against the question

number on the OMR answer sheet

Correct Method of shading the circle on the OMR answer sheet is as shown below

A B C D

4 Please note that even a minute unintended ink dot on the OMR answer sheet will also be recognized and recorded by the scanner Therefore avoid multiple markings of any kind on the OMR answer sheet

5 Use the space provided on the question booklet for Rough Work Do not use the OMR answer sheet for the same

6 After the last bell is rung at 500 pm stop writing on the OMR answer sheet and affix your left hand thumb impression on the OMR answer sheet as per the instructions

7 Hand over the OMR answer sheet to the room invigilator as it is 8 After separating the top sheet the invigilator will return the bottom sheet replica (candidatersquos copy) to you to

carry home for self evaluation 9 Preserve the replica of the OMR answer sheet for a minimum period of ONE year 10 In case of any discrepancy in the English and Kannada Versions the English version will be taken as final in case

of Compulsory Paper ndash III and Optional Papers except the languages of optional paper

GFGC

Space For Rough Work

2 Physics

1 If A and B are the two non-parallel vectors and have equal magnitude then the angle between the vectors (A + B) and (A ndash B) must be

(A) 180deg (B) 90deg (C) Less than 90deg (D) Greater than 90deg A ordfAgraveAumlvAgraveAumlUcirc B UAgravefrac14AgraveAuml JgAgraveqAgraveAuml cedilAgraveordfAgraveAumlpoundAacuteAvAgravegAgraveordfAgraveregegravezAgrave cedilAgravecentplusmnAgraveUAgravefrac14AacuteVzAgraveAumlYacute cedilAgraveordfAgraveiAacutepoundAgrave yenAgraveaeligordfAgraveiAacutetordfAgravepoundAgraveAumlszlig

ordmEacuteAEligAcentzAgraveYacutegEacute DUAgrave (A + B) ordfAgraveAumlvAgraveAumlUcirc (A ndash B) cedilAgravecentplusmnAgraveUAgravefrac14Agrave poundAgraveqAgraveAumllaquopoundAgrave PEacuteAEligAtildepoundAgrave (A) 180deg (B) 90deg (C) 90deg VAvAgrave PAgraverordfEacuteAuml (D) 90deg VAvAgrave ordmEacuteZAgraveAumlNtilde 2 Newtonrsquos law of force can be stated as

(A) dt

dpF = (B)

dt

dF

x=

(C) dt

dvF = (D)

dt

daF =

Here p is the momentum x the displacement v the velocity and a the acceleration poundAgraveAEligaringlpoundiumlpoundAgrave sectregzAgrave currenAiAgraveAumlordfAgraveAumlordfAgravepoundAgraveAumlszlig raquoAtildeUEacuteAzAgraveAuml ordmEacuteAtildefrac14AgravesectordmAgraveAumlzAgraveAuml

(A) dt

dpF = (B)

dt

dF

x=

(C) dt

dvF = (D)

dt

daF =

Edegegrave p AiAgraveAumlAuml cedilAgraveAordfEacuteAtildeUAgrave x MAzAgraveAuml cedilAacuteUumlpoundAgraveyenAgraveregegravel v AiAgraveAumlAuml ordfEacuteAtildeUAgraveordfAacuteVzAgraveAumlYacute ordfAgraveAumlvAgraveAumlUcirc a ordfEacuteAtildeUEacuteAEligAtildevAgraveIgravemicroAgraveethordfAacuteVzEacute

3 The Coriolis force on a moving particle will be (A) Perpendicular to ω and v (B) Parallel to ω and v (C) Parallel to ω and Perpendicular to v (D) Perpendicular to ω and Parallel to v Here ω and v are the angular and linear velocities respectively MAzAgraveAuml ZAgravedegcedilAgraveAumlordfAgrave PAgravetzAgrave ordfEacuteAumlAtilde5Eacute PEacuteAEligjAiAgraveiAacutedegcediliuml sectregordfAgraveAring F PEacutefrac14AgraveVpoundAgraveAwgAgraveAumlvAgraveUcirczEacute (A) ω ordfAgraveAumlvAgraveAumlUcirc v UAgravefrac12UEacute regAsect (B) ω ordfAgraveAumlvAgraveAumlUcirc v UEacute cedilAgraveordfAgraveAumlpoundAacuteAvAgravegAgrave (C) ω UEacute cedilAgraveordfAgraveAumlpoundAacuteAvAgravegAgrave ordfAgraveAumlvAgraveAumlUcirc v UEacute regAsect (D) ω UEacute regAsect ordfAgraveAumlvAgraveAumlUcirc v cedilAgraveordfAgraveAumlpoundAacuteAvAgravegAgrave Edegegrave ω ordfAgraveAumlvAgraveAumlUcirc v PAgraveaeligordfAgraveAumlordfAacuteV PEacuteAEligcurrenAtildeAiAgraveAuml ordmAacuteUAgraveAElig gEacuteAtildeTAtildeAiAgraveAuml ordfEacuteAtildeUAgraveUAgravefrac14AacuteVgAgraveAumlvAgraveUcircordfEacute


Physics 3

4 Poissonrsquos ratio is defined in terms of lateral strain β and longitudinal strain α as yenAacutenotAumlUumlEgravearingpoundiuml currenmicroAgraveagravewUcircAiAgraveAumlpoundAgraveAumlszlig yenAacuteplusmnAgraveetheacute laquoPAgraveEgravew (β) ordfAgraveAumlvAgraveAumlUcirc gEacuteAtildeSAacuteAsup2AtildeAiAgraveAuml laquoPAgraveEgravew (α) UAgravefrac14AgravepoundAgraveAumlszlig sectfrac14Agravesup1

F PEacutefrac14AgraveVpoundAgraveAvEacute ordfAacutearingSAacutearingcurrencedilAgravesectordmAgraveAumlzAgraveAuml (A) (αβ) (B) (αβ) (C) (α+β) (D) (βα)

5 Surface tension is a property of (A) Solid (B) Liquid (C) Gas (D) Plasma ordfEacuteAumlAtilde5EacuteaumloumlEcirc Jfrac14EacutevAgraveordfAgraveAring F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgraveAringzAgravegAgrave UAgraveAumltzsAgraveordfAgraveAumlethordfAacuteVzEacute (A) WAgravepoundAgrave (B) zAgraveaeligordfAgrave (C) Ccurrenreg (D) yensAacuteegravecedilAgraveauml

6 The period of revolution of a geostationary satellite must be (A) Equal to the period of rotation of earth (B) Equal to the twice the period of rotation of earth (C) Equal to the three times the period of rotation of earth (D) Equal to the period of rotation of sun sAgraveAEligcedilAacuteUumlnotAuml GyenAgraveUAgraveaeligordmAgravezAgrave yenAgravej sAgraveaeligordfAgraveAumluEacuteAiAgraveAuml CordfAgravecentuumlAiAgraveAumlAuml (A) sAgraveAEliglaquoAumlAiAgraveAuml sAgraveaeligordfAgraveAumluEacuteAiAgraveAuml CordfAgravecentuumlUEacute cedilAgraveordfAgraveAumlpoundAacuteVgAgraveAumlvAgraveUcirczEacute (B) sAgraveAEliglaquoAumlAiAgraveAuml sAgraveaeligordfAgraveAumluEacuteAiAgraveAuml CordfAgravecentuumlAiAgraveAuml JgAgraveqAgraveAuml yenAgravelAumlOuml cedilAgraveordfAgraveAumlpoundAacuteVgAgraveAumlvAgraveUcirczEacute (C) sAgraveAEliglaquoAumlAiAgraveAuml sAgraveaeligordfAgraveAumluEacuteAiAgraveAuml CordfAgravecentuumlAiAgraveAuml ordfAgraveAumlAEliggAgraveAuml yenAgravelAumlOuml cedilAgraveordfAgraveAumlpoundAacuteVgAgraveAumlvAgraveUcirczEacute (D) UumlEgravearingeumlsup2igravearingecirccurrenAumlaring sAgraveaeligordfAgraveAumluEacuteAiAgraveAuml CordfAgravecentuumlUEacute cedilAgraveordfAgraveAumlpoundAacuteVgAgraveAumlvAgraveUcirczEacute

7 Work done per mol in an isothermal expansion of a vander Waals gas from volume V1 to V2

ordfAacutearingpoundAgraveOslashgiuml ordfAacute5iumlpoundAgrave CcurrenregordfAgraveAring UAacutevAgraveaelig V1 jAzAgrave V2 UEacute cedilAgraveordfEacuteAEligAtildemicroAgraveUacutevAacute ordfAacutearingPEacuteAEligAtildeZAgravepoundAgraveUEacuteAEligAqAacuteUAgrave Cdegegrave poundAgraveqEacuteAiAgraveAumlAumlordfAgrave PAacuteAiAgraveAumlethzAgrave ordfEacuteAEligvAgraveUcirc

(A)

minus+

minus

minus

121

2 11ln

VVa

bV

bVRT

(B)

minus+

minus

minus

212

1 11ln

VVa

bV

bVRT

(C)

minus

minus

+

minus

bV

bVa

VVRT

1

2

12

11ln

(D)

minus

minus

+

minus

bV

bVa

VVRT

2

1

21

11ln


4 Physics

8 Helium exhibits (A) Triple point at 42 K (B) Triple point at 14 K (C) Triple point at 42 K (D) 0 K raquoAtildedegAiAgraveAumlA F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgraveAringzAgravepoundAgraveAumlszlig ordfAgravearingPAgraveUcircyenAgravercedilAgraveAumlvAgraveUcirczEacute (A) 42 K AiAgraveAumldegegrave waeligcopyAzAgraveAuml (B) 14 K AiAgraveAumldegegrave waeligcopyAzAgraveAuml (C) 42 K AiAgraveAumldegegrave waeligcopyAzAgraveAuml (D) 0 K

9 It is impossible to construct a device which transfers heat energy completely from a colder

body to a hotter body without any other effect This is the (A) Statement of zeroth law of thermodynamics (B) Statement of first law of thermodynamics (C) Statement of second law of thermodynamics (D) Statement of third law of thermodynamics sup2AtildevAgrave ordfAgravecedilAgraveAumlUcirclaquocurrenAzAgrave GmicroAgraveUacute ordfAgravecedilAgraveAumlUcirclaquoUEacute GmicroAgraveUacuteplusmnAgraveQUcircAiAgraveAumlpoundAgraveAumlszlig EvAgravegEacute AiAgraveiAacuteordfAgraveAringzEacuteAtilde yenAgravejuAacuteordfAgraveAumllaquoregegravezEacute

cedilAgraveAyenAgraveAEligtethordfAacuteV ordfAgraveUAacuteethnotAumlcedilAgraveAumlordfAgrave cedilAacutezsAgravepoundAgraveordfAgravepoundAgraveAumlszlig gAgraveacedilAgraveregAuml cedilAacutezsAgravearinglaquoregegrave EzAgraveAuml F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgrave currenAiAgraveAumlordfAgraveAumlordfAacuteVgAgraveAumlvAgraveUcirczEacute

(A) GmicroAgraveUacute sectreg laquoeAacuteOtildepoundAgravezAgrave fAtildegEacuteAEligAtildeviuml currenAiAgraveAumlordfAgraveAuml (B) GmicroAgraveUacute sectreg laquoeAacuteOtildepoundAgravezAgrave ordfEacuteAEligzAgraveregpoundEacuteAtilde currenAiAgraveAumlordfAgraveAuml (C) GmicroAgraveUacute sectreg laquoeAacuteOtildepoundAgravezAgrave JgAgraveqAgravepoundEacuteAtilde currenAiAgraveAumlordfAgraveAuml (D) GmicroAgraveUacute sectreg laquoeAacuteOtildepoundAgravezAgrave ordfAgraveAumlAEliggAgravepoundEacuteAtilde currenAiAgraveAumlordfAgraveAuml 10 Which one of the following statement is wrong (A) There can be no negative temperature on the Kelvin absolute scale (B) Carnot engine produces more mechanical work energy than heat energy that it

absorbs from source (C) Absolute zero is the lowest temperature of any substance (D) Efficiency of Carnot engine cannot be more than unity F PEacutefrac14AgraveVpoundAgrave ordmEacuteAtildefrac12PEacuteUAgravefrac14Agravedegegrave AiAgraveiAacuteordfAgraveAringzAgraveAuml vAgraveyenAgraveAumlagrave (A) PEacutedegeacutepoundiuml currengAgraveyenEacuteAtildePAgraveeuml ordfAgraveiAacutepoundAgravePAgravezAgrave ordfEacuteAumlAtilde5Eacute AiAgraveiAacuteordfAgraveAringzEacuteAtilde IAumluAacutevAgraveaumlPAgrave GmicroAgraveUacutevEacuteAiAgraveAuml EgAgraveAumllaquoPEacute

cedilAacutezsAgravearinglaquoregegrave (B) PAacutepoundAacuteethmiuml EAfpoundiuml vAacutepoundAgraveAuml ordfAgraveAumlAEligregcentAzAgrave raquoAtildejPEacuteAEligfrac14AgraveAumlicircordfAgrave GmicroAgraveUacuteplusmnAgraveQUcircVAvAgrave ordmEacuteZAgraveAumlNtilde

AiAgraveiAacuteAwaeligPAgrave PAacuteAiAgraveAumlethordfAgravepoundAgraveAumlszlig GvAacuteagravecentcedilAgraveAumlvAgraveUcirczEacute (C) currengAgraveyenEacuteAtildePAgraveeuml plusmnAgraveAEligpoundAgravearingordfAgraveAring AiAgraveiAacuteordfAgraveAringzEacuteAtilde yenAgravezAacutexAgraveethzAgrave Cw PAgravecurrenmicroAgraveOuml GmicroAgraveUacutevEacuteAiAgraveiAacuteVzEacute (D) PAacutepoundAacuteethmiuml EAfpoundiumlpoundAgrave cedilAacuteordfAgraveAumlxAgraveetharingordfAgraveAring MAzAgraveQIgraveAvAgrave ordmEacuteaNtildegAgraveregAuml cedilAacutezsAgravearinglaquoregegrave


Physics 5

11 Second order phase transitions (A) Occur across the phase equilibrium curves (B) Involve latent heat (C) Can be described by the Clausius-Claperon equations (D) Are associated with discontinuities in compressibility and expansivity centeacutewAtildeAiAgraveAuml PAgraveaeligordfAgraveAuml CordfAgravecedilAacuteUuml cedilAgraveAPAgraveaeligordfAgraveAumltUAgravefrac14AgraveAuml (A) CordfAgravecedilAacuteUuml cedilAgraveordfAgraveAumlvEacuteAEligAtilderegpoundAgrave ordfAgravePAgraveaeligUAgravefrac14Agrave ordfEacuteAumlAtilde5Eacute poundAgraveqEacuteAiAgraveAumlAumlvAgraveUcirczEacute (B) UAgraveAumlyenEacuteAEligUcircAtildemicroAgraveUacuteordfAgravepoundAgraveAumlszlig Mfrac14AgraveUEacuteAEligArgAgraveAumlvAgraveUcirczEacute (C) PAacuteegravesup1AiAgraveAumlcediliuml-PAacuteegraveyenEacutegAacutepoundiuml cedilAgravelaquoAumlAtildePAgravegAgravetUAgravefrac12AzAgrave ordfAgravetAcircethcedilAgravesectordmAgraveAumlzAgraveAuml (D) cedilAgraveAbrvbarAtildeqAgravepoundAacutesup2AtilderegvEacute ordmAacuteUAgraveAElig laquocedilAacuteUcircgAgraveordfAacuteUAgraveAumllaquoPEacuteAiAgraveAumldegegrave laquoaOgravepoundAgraveszligvEacute˜microaringfrac14EacuteAEligAcentUEacute

cedilAgraveAAiEacuteAEligAtildedpoundEacuteUEacuteAEligArgAgraveAumlvAgraveUcirczEacute 12 To represent a point for a N-molecule system we require to have (A) 3N position coordinates (B) 3N momentum coordinates (C) 3N position coordinates and 3N momentum coordinates (D) 6N position coordinates

N-CtAuml ordfAgravearingordfAgravecedilEacuteUumlUEacute copyAzAgraveAuml cedilAgraveUumlfrac14AgraveordfAgravepoundAgraveAumlszlig vEacuteAEligAtildejcedilAgraveregAuml poundAgraveordfAgraveAumlUEacute umlEacuteAtildePAacutezAgraveAumlzAgraveAuml (A) 3N cedilAacuteUumlpoundAgrave yenAgraveaeligordfAgraveiAacutetPAgrave currenzEacuteethAtildeplusmnAacuteAPAgraveUAgravefrac14AgraveAuml (B) 3N cedilAacuteUumlpoundAgrave DordfEacuteAtildeUAgrave currenzEacuteethAtildeplusmnAacuteAPAgraveUAgravefrac14AgraveAuml (C) 3N cedilAacuteUumlpoundAgrave yenAgraveaeligordfAgraveiAacutetPAgrave ordfAgraveAumlvAgraveAumlUcirc 3N DordfEacuteAtildeUAgrave currenzEacuteethAtildeplusmnAacuteAPAgraveUAgravefrac14AgraveAuml (D) 6N cedilAacuteUumlpoundAgrave yenAgraveaeligordfAgraveiAacutetPAgrave currenzEacuteethAtildeplusmnAacuteAPAgraveUAgravefrac14AgraveAuml 13 Bosons and Fermions can be described by (A) Symmetric and anti-symmetric wave functions respectively (B) Anti-symmetric and symmetric wave functions respectively (C) Symmetric wave functions only (D) Anti-symmetric wave functions only umlEacuteAEligAtildecedilAacutepoundiumligrave ordfAgraveAumlvAgraveAumlUcirc yensAgravelaquoAumlethAiAgraveiAacutepoundiumligrave UAgravefrac14AgravepoundAgraveAumlszlig AiAgraveiAacuteordfAgraveAringzAgravejAzAgrave laquoordfAgravejcedilAgravesectordmAgraveAumlzAgraveAuml (A) CpoundAgraveAumlPAgraveaeligordfAgraveAumlordfAacuteV cedilAgraveordfAgraveAumlaumlw ordmAacuteUAgraveAElig yenAgraveaeligwcedilAgraveordfAgraveAumlaumlwAtildeAiAgraveAuml vAgravegAgraveAUAgrave yensAgraveregpoundAgraveUAgravefrac14AgraveAuml (B) CpoundAgraveAumlPAgraveaeligordfAgraveAumlordfAacuteV yenAgraveaeligwcedilAgraveordfAgraveAumlaumlwAtildeAiAgraveAuml ordmAacuteUAgraveAElig cedilAgraveordfAgraveAumlaumlw vAgravegAgraveAUAgrave yensAgraveregpoundAgraveUAgravefrac14AgraveAuml (C) cedilAgraveordfAgraveAumlaumlw vAgravegAgraveAUAgrave yensAgraveregpoundAgraveUAgravefrac14AgraveAuml ordfAgraveiAacutevAgraveaelig (D) yenAgraveaeligwcedilAgraveordfAgraveAumlaumlwAtildeAiAgraveAuml vAgravegAgraveAUAgrave yensAgraveregpoundAgraveUAgravefrac14AgraveAuml ordfAgraveiAacutevAgraveaelig


6 Physics

14 Fermi-Dirac statistical distribution function is applicable to the following set of particles

(A) Electrons Protons (B) Photons Phonons

(C) Gas molecules magnons (D) Gravitons excitons

yensAgravelaquoAumleth-rgAacutePiuml cedilAacuteOumloumlaringnsup1OumlPAgrave5iuml ordmAgravegAgraveqAgraveAumllaquoPEacute currenAiAgraveAumlordfAgraveAumlordfAgraveAring F PEacutefrac14AgravePAgraveAqAgrave AiAgraveiAacuteordfAgrave PAgravetUAgravefrac14Agrave UAgravetPEacuteIgrave CpoundAgraveeacutenotAumlcedilAgraveAumlvAgraveUcirczEacute

(A) J5EacutePAacuteOumlccedilpoundiumlUAgravefrac14AgraveAuml yenEacuteAEligaeligAtildemAacutepoundiumlUAgravefrac14AgraveAuml

(B) yenEacuteAEligaeligAtildemAacutepoundiumlUAgravefrac14AgraveAuml yensEacuteAEligAtildepoundAacutepoundiumlUAgravefrac14AgraveAuml

(C) UAacutearingcediliuml ordfAgraveiAacutedegPAgraveAEligaring5iumlUAgravefrac14AgraveAuml ordfAgraveiAacutearingUAacuteszligpoundiumlUAgravefrac14AgraveAuml

(D) UAacuteaeliglaquoAtildemAacutepoundiumlUAgravefrac14AgraveAuml JldquoTHORNmAacutepoundiumlUAgravefrac14AgraveAuml

15 As per Bose-Einstein statistics the number of particles in an ith state is given by

umlEacuteAEligAtildecediliuml-LpoundiumlcedilEacuteOumloumlEcircpoundiuml cedilAacuteOumloumlaringnsup1OumlPiumligrave yenAgraveaeligPAacutegAgrave ith sup1UumlwAiAgraveAumldegegrave PAgravetUAgravefrac14Agrave cedilAgraveASEacutearing F PEacutefrac14AgraveVpoundAgraveAvEacute EgAgraveAumlvAgraveUcirczEacute

(A)

+

=

)exp( i

ii

E

gn

βα

(B)

minus+

=

1)exp( i

ii

E

gn

βα

(C)

++

=

1)exp( i

ii

E

gn

βα

(D)

+minus

=

)exp(1 i

ii

E

gn

βα

16 Microcanonical ensemble is a collection of independent systems having the same

(A) Energy volume and number of particles

(B) Temperature volume and number of particles

(C) Temperature volume and chemical potential

(D) Energy volume and chemical potential

ordfEacuteAumlEcircPEacuteAEligaeligAtildePAacutearingpoundEacuteAEligAtildecurrenPAgrave5iuml JpoundEacuteigraveAsect5iuml EzAgraveAuml MAzEacuteAtilde vEacutegAgravepoundAacutezAgrave F PEacutefrac14AgraveVpoundAgrave ordfAgravearingordfAgravecedilEacuteUumlAiAgraveAumlAumlfrac14Agraveicirc cedilAgraveeacutevAgraveAvAgraveaelig ordfAgravearingordfAgravecedilEacuteUumlAiAgraveAuml cedilAgraveAUAgraveaeligordmAgravetordfAacuteVzEacute

(A) plusmnAgraveQUcircUcirc UAacutevAgraveaelig ordfAgraveAumlvAgraveAumlUcirc PAgravetUAgravefrac14Agrave cedilAgraveASEacutearing

(B) GmicroAgraveUacutevEacute UAacutevAgraveaelig ordfAgraveAumlvAgraveAumlUcirc PAgravetUAgravefrac14Agrave cedilAgraveASEacutearing

(C) GmicroAgraveUacutevEacute UAacutevAgraveaelig ordfAgraveAumlvAgraveAumlUcirc gAacutecedilAacuteAiAgraveAumlcurrenPAgrave laquo sAgraveordfAgrave

(D) plusmnAgraveQUcirc UAacutevAgraveaelig ordfAgraveAumlvAgraveAumlUcirc gAacutecedilAacuteAiAgraveAumlcurrenPAgrave laquo sAgraveordfAgrave


Physics 7

17 For Bosons below Bose-Einstein condensation temperature the number of particles in the

momentum state p will

(A) tend to maximum as temperature tend to absolute zero

(B) tend to minimum as temperature tend to absolute zero

(C) remain constant as temperature tend to absolute zero

(D) be zero

umlEacuteAEligAtildecediliuml-LpoundiumlcedilEacuteOumloumlEcircpoundiuml cedilAacuteAcentaeligPAgravegAgravet GmicroAgraveUacutevEacuteAiAgraveAuml PEacutefrac14AgraveUEacute umlEacuteAEligAtildecedilAacutepoundiumligraveUEacute cedilAgraveAordfEacuteAtildeUAgrave sup1UumlwAiAgraveAumldegegravepoundAgrave

PAgravetUAgravefrac14Agrave cedilAgraveASEacutearing P sup2igravearingecircecirc

(A) GmicroAgraveUacutevEacuteAiAgraveAumlAuml currengAgraveyenEacuteAtildePAgraveeuml plusmnAgraveAEligpoundAgravearingordfAacutezAgraveAvEacute ordmEacuteZAacuteNtildeUAgraveAumlvAgraveUcirczEacute

(B) GmicroAgraveUacutevEacuteAiAgraveAumlAuml currengAgraveyenEacuteAtildePAgraveeuml plusmnAgraveAEligpoundAgravearingordfAacutezAgraveAvEacute PAgraverordfEacuteAumlAiAgraveiAacuteUAgraveAumlvAgraveUcirczEacute

(C) GmicroAgraveUacutevEacuteAiAgraveAumlAuml currengAgraveyenEacuteAtildePAgraveeuml plusmnAgraveAEligpoundAgravearingordfAacutezAgraveAvEacute sup1UumlgAgraveordfAacuteVgAgraveAumlvAgraveUcirczEacute

(D) plusmnAgraveAEligpoundAgravearingordfAacuteVgAgraveAumlvAgraveUcirczEacute

18 Planckrsquos law for black body radiation is given as

PAgraveEgravemicroAgraveUacutePAacuteAiAgraveAuml laquoQgAgravetPEacuteIgrave yensAacuteegraveoumlaringAPiumlpoundAgrave currenAiAgraveAumlordfAgraveAumlordfAgraveAring F PEacutefrac14AgraveVpoundAgraveAwgAgraveAumlvAgraveUcirczEacute

(A) [ ]1)exp(

8 3

minus

=

minus

Tkhc

hcE

Bλ

λπ (B)

[ ]1)exp(

8 5

+

=

minus

Tkhc

hcE

Bλ

λπ

(C) [ ]1)exp(

8 3

+

=

minus

Tkhc

hcE

Bλ

λπ (D)

[ ]1)exp(

8 5

minus

=

minus

Tkhc

hcE

Bλ

λπ

19 A particle is executing SHM with a period of 0001 s and amplitude of 005 m Its

acceleration is

MAzAgraveAuml PAgravetordfAgraveAring 0001 s CordfAgravecentuuml ordfAgraveAumlvAgraveAumlUcirc 005 m yenAacutegAgraveordfEacuteEcircplusmnAacuteregaringzEacuteAEligAcentUEacute cedilAgravegAgravefrac14Agrave cedilAgraveAUAgravevAgrave ZAgraveregpoundEacuteAiAgraveAumldegegravegAgraveAumlordfAacuteUAgrave CzAgravegAgrave ordfEacuteAtildeUEacuteAEligAtildevAgraveIgravemicroAgraveethordfAgraveAring F PEacutefrac14AgraveVpoundAgraveparaOumlgAgraveAumlvAgraveUcirczEacute

(A) 79 times 104 ms2 (B) 5 times 10ndash5 ms2

(C) 50 ms2 (D) 002 ms2


8 Physics

20 Beats are observed when the two sound waves travelling in the same direction are superimposed on each other having

(A) Different amplitude and same wavelength (B) Same amplitude and different wavelength (C) Same amplitude and same phase (D) Different amplitude and different wavelength F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgraveAringzAgravepoundAgraveAumlszlig Mfrac14AgraveUEacuteAEligAqAgraveAuml MAzEacuteAtilde centQIgravepoundAgravedegegrave ZAgravedegcedilAgraveAumlwUcircgAgraveAumlordfAgrave JgAgraveqAgraveAuml zsAgraveeacutecurren

vAgravegAgraveAUAgraveUAgravefrac14AgraveAuml MAzAgravegAgrave ordfEacuteAumlAtilde5EacuteAEligAzAgraveAuml CzsAacutearinggEacuteAEligAtildebrvbarvAgraveUEacuteAEligAqAacuteUAgrave copyAtildemiumlUAgravefrac14AgravepoundAgraveAumlszlig PAacutetsectordmAgraveAumlzAgraveAuml (A) copyuumlpoundAgraveszlig yenAacutegAgraveordfEacuteEcircplusmnAacuteregaring ordfAgraveAumlvAgraveAumlUcirc MAzEacuteAtilde vAgravegAgraveAUAacuteAvAgravegAgrave (B) MAzEacuteAtilde yenAacutegAgraveordfEacuteEcircplusmnAacuteregaring ordfAgraveAumlvAgraveAumlUcirc copyuumlpoundAgraveszlig vAgravegAgraveAUAacuteAvAgravegAgrave (C) MAzEacuteAtilde yenAacutegAgraveordfEacuteEcircplusmnAacuteregaring ordfAgraveAumlvAgraveAumlUcirc MAzEacuteAtilde vAgravegAgraveAUAacuteAvAgravegAgrave (D) copyuumlpoundAgraveszlig yenAacutegAgraveordfEacuteEcircplusmnAacuteregaring ordfAgraveAumlvAgraveAumlUcirc copyuumlpoundAgraveszlig vAgravegAgraveAUAacuteAvAgravegAgrave

21 Two trains are approaching each other with the speed of 60 kmh and 45 kmh A whistle of frequency 512 Hz is sounded by the first train The frequency of the note heard by a listener in the second train before passing each other is

JgAgraveqAgraveAuml gEacuteEcircregAumlUAgravefrac14AgraveAuml yenAgraveaeligwUAgraveAmEacuteUEacute 60 QlaquoAumlAtilde ordfAgraveAumlvAgraveAumlUcirc 45 QlaquoAumlAtilde ordfEacuteAtildeUAgravezEacuteAEligAcentUEacute CcopyuumlordfAgraveAumlAumlRordfAacuteV ZAgravedegcedilAgraveAumlwUcircordfEacute ordfEacuteAEligzAgraveregpoundEacuteAtilde gEacuteEcircregAuml 512 Hz DordfAgravevAacuteethAPAgravezAgrave sup2frac14Eacuteicirc ordmAacuteQzEacute gEacuteEcircregAumlUAgravefrac14AgraveAuml MAzAgravePEacuteAEligIgraveAzAgraveAuml cedilAgraveAcentuumlsup1 ordmAacutezAgraveAumlordmEacuteAEligAtildeUAgraveAumlordfAgrave ordfAgraveAumlAumlpoundAgraveszlig JgAgraveqAgravepoundEacuteAtilde gEacuteEcircdegpoundAgravedegegravegAgraveAumlordfAgrave PEacuteAtildefrac14AgraveAumlUAgravecurrenUEacute PEacuteAtildefrac14AgraveregagravelOuml cedilAgraveeacutegAgravezAgrave DordfAgravevAacuteethAPAgraveordfAgraveAring

(A) 5593 Hz (B) 5593 Hz (C) 5593 Hz (D) 5593 Hz

22 The time of reverberation of the empty auditorium is T The time of reverberation of the auditorium with the curtains and floor mats will be

(A) Larger than T (B) Less than T (C) Same as T (D) Zero MAzAgraveAuml SAacutedeg cedilAgrave sAacuteAUAgravetzAgrave yenAgraveaeligwgAgravetpoundAgravezAgrave CordfAgravecentuumlAiAgraveAumlAuml T DVzEacute ordmAacuteUAacutezAgravegEacute yenAgravegAgravezEacuteUAgravefrac14AgraveAuml ordfAgraveAumlvAgraveAumlUcirc

poundEacuteregordmAacutecedilAgraveAumlUAgravefrac14AgravepoundAgraveAumlszlig ordmEacuteAEligAcentgAgraveAumlordfAgrave cedilAgrave sAacuteAUAgravetzAgrave yenAgraveaeligwgAgravetpoundAgravezAgrave cedilAgraveordfAgraveAumlAiAgraveAumlordfAgraveAring (A) T VAvAgrave ordmEacuteZAacuteNtildeVgAgraveAumlvAgraveUcirczEacute (B) T VAvAgrave PAgraverordfEacuteAumlAiAgraveiAacuteVgAgraveAumlvAgraveUcirczEacute (C) T AiAgraveAumlmicroEacuteOumlAtilde EgAgraveAumlvAgraveUcirczEacute (D) plusmnAgraveAEligpoundAgravearingordfAacuteVgAgraveAumlvAgraveUcirczEacute

23 In vacuum light travels at a speed of 3 times 108 ms What is the speed of light in a glass of refractive index 15

currenordfAacuteethvAgravezAgravedegegrave umlEacutefrac14AgravePAgraveAuml 3 times 108 ms ordfEacuteAtildeUAgravezAgravedegegrave ZAgravedegsup1zAgravegEacute MAzAgraveAuml ordfAgraveQaeligAtilde sAgraveordfAgravepoundAacuteAPAgrave 15 gAgrave UAacutefpoundAgravedegegrave umlEacutefrac14AgraveQpoundAgrave ordfEacuteAtildeUAgrave JparaOumlgAgraveAumlvAgraveUcirczEacute

(A) 10 times 108 ms (B) 45 times 108 ms (C) 2 times 108 ms (D) 3 times 108 ms


Physics 9

24 In a given media in which one of the following colour order the speed of light increases (A) Blue Green Yellow Red (B) Red Yellow Green Blue (C) Green Red Blue Yellow (D) Green Blue Orange Red PEacuteAElignOumlgAgraveAumlordfAgrave ordfAgraveiAacutezsAgravearingordfAgraveAumlzAgravedegegrave F PEacutefrac14AgravePAgraveAqAgrave AiAgraveiAacuteordfAgraveAringzAgraveAuml umlEacutefrac14AgraveQpoundAgrave ordfEacuteAtildeUAgraveordfAgravepoundAgraveAumlszlig DgEacuteAEligAtildeordmAgravet PAgraveaeligordfAgraveAumlzAgravedegegrave

PEacuteAEligqAgraveAumlvAgraveUcirczEacute (A) currenAtildedeg ordmAgravesup1gAgraveAuml ordmAgravefrac14Agravecent PEacuteAyenAgraveAuml (B) PEacuteAyenAgraveAuml ordmAgravefrac14Agravecent ordmAgravesup1gAgraveAuml currenAtildedeg (C) ordmAgravesup1gAgraveAuml PEacuteAyenAgraveAuml currenAtildedeg ordmAgravefrac14Agravecent (D) ordmAgravesup1gAgraveAuml currenAtildedeg QvAgraveUcircfrac14Eacute PEacuteAyenAgraveAuml

25 Light travels with speed of 2 times 108 ms in crown glass of refractive index 15 What is the speed of light in dense flint glass of refractive index 18

ordfAgraveQaeligAtilde sAgraveordfAgravepoundAacuteAPAgrave cedilAgraveAEliga 15 EgAgraveAumlordfAgrave PEumlaeligpoundiuml UAacutefpoundAgravedegegrave umlEacutefrac14AgravePAgraveAuml 2 times 108 ms ordfEacuteAtildeUAgravezAgravedegegrave ZAgravedegcedilAgraveAumlvAgraveUcirczEacute ordmAacuteUAacutezAgravegEacute ordfAgraveQaeligAtilde sAgraveordfAgravepoundAacuteAPAgrave cedilAgraveAEliga 18 gAgrave qEacutepoundiumligraveCcedilmiddotYacuteugraveugraveOacuteAmiuml UAacutefpoundAgravedegegrave umlEacutefrac14AgraveQpoundAgrave ordfEacuteAtildeUAgrave JmicroAacuteOumlVgAgraveAumlvAgraveUcirczEacute


26 What is the effect on the interference fringes in Youngrsquos double slit experiment if the width of the sources slit is increased

(A) The fringe width increases (B) The fringe become less distinct (C) The fringe width decreases (D) The fringe become more distinct DPAgravegAgraveUAgravefrac14Agrave sup1Atildefrac12poundAgrave CUAgraveregordfAgraveAring ordmEacuteZAacuteNtildezAgravegEacute lsquoAiAgraveAumlAUiumlrsquopoundAgrave centeacute-sup1Atildefrac14AgraveAuml yenAgraveaeligAiEacuteAEligAtildeUAgravezAgravedegegrave ordfAgravearingwPAgravegAgravet

brvbaraeligAeiumlUAgravefrac14Agrave ordfEacuteAumlAtildedegpoundAgrave yenAgravejuAacuteordfAgraveAumlordfEacuteAtildepoundAgraveAuml (A) brvbaraeligAeiumlpoundAgrave CUAgraveregordfAgraveAring ordmEacuteZAacuteNtildeUAgraveAumlvAgraveUcirczEacute (B) brvbaraeligAeiumlpoundAgrave cedilAgraveagravemicroAgraveOumlvEacuteAiAgraveAumlAuml PAgraverordfEacuteAumlAiAgraveiAacuteUAgraveAumlvAgraveUcirczEacute (C) brvbaraeligAeiumlpoundAgrave CUAgraveregordfAgraveAring PAgraverordfEacuteAumlAiAgraveiAacuteUAgraveAumlvAgraveUcirczEacute (D) brvbaraeligAeiumlpoundAgrave cedilAgraveagravemicroAgraveOumlvEacuteAiAgraveAumlAuml ordmEacuteZAacuteNtildeUAgraveAumlvAgraveUcirczEacute

27 Which one of the following waves cannot be polarized (A) Radio waves (B) Longitudinal waves (C) X- rays (D) Transverse waves F PEacutefrac14AgravePAgraveAqAgrave AiAgraveiAacuteordfAgrave vAgravegAgraveAUAgraveUAgravefrac14AgravepoundAgraveAumlszlig zAgraveEgravelaquoAtildePAgravejcedilAgrave5AacuteUAgravezAgraveAuml (A) gEacuteAtilderAiEacuteAEligAtilde vAgravegAgraveAUAgraveUAgravefrac14AgraveAuml

(B) CcurrenregzAgravedegegraveAiAgraveAuml currenAtildefrac14Agrave gEacuteAtildeSEacuteUAgravefrac14AgraveAuml (sup2microetheacutebullyumlaeligOgravetimesaringAacutemicroaring frac14aringsup2microaringOgrave˜microaring microaringacircyumlaringecirc) (C) PAgraveeuml-QgAgravetUAgravefrac14AgraveAuml

(D) sup1OumlccedilAUiumlpoundAgravedegegravepoundAgrave CqAgraveOslash (macraeligETHAumloacuteTHORNOcircaringUumlEgraveoacutecurren) vAgravegAgraveAUAgraveUAgravefrac14AgraveAuml


10 Physics

28 The electric field at a point P inside a uniformly charged sphere of radius R is given by (the point P is situated at a distance lsquorrsquo from the center of the sphere)

KPAgravejAtildewAiAgraveiAacuteV yenAgraveAEliggAgravetUEacuteAEligAqAgrave UEacuteAEligAtildefrac14AgravezAgrave waeligdaring R poundAgravedegegrave copyAzAgraveAuml P AiAgraveAuml laquozAgraveAumlaringviuml PEacuteeumlAtildevAgraveaeligordfAgravepoundAgraveAumlszlig F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgrave cedilAgravelaquoAumlAtildePAgravegAgravetcentAzAgrave PAgraveAqAgraveAumlraquorAiAgraveAumlsectordmAgraveAumlzAgraveAuml (copyAzAgraveAuml P sup2igravearingecircecirc UEacuteAEligAtildefrac14AgravezAgrave PEacuteAtildeAzAgraveaeligcentAzAgrave lsquorrsquo poundAgrave CAvAgravegAgravezAgravedegegravezEacute)

(A) ρ

ε0 (B)

ρ

3ε0

(C) 4πr3

3 ρ

ε0 (D)

rρ

3ε0

29 The differential form of Faraday law is yensAacutearinggEacuteqEacute currenAiAgraveAumlordfAgraveAumlzAgrave CordfAgravePAgraveregpoundAgrave gAgraveAEligyenAgraveordfAgraveAring

(A) nabla rarr

E = 0 (B) nabla times

rarr

E = 0

(C) nabla times

rarr

E = ndash part

rarr

B

partt (D) nabla

rarr

E = ρ

30 The Poissonrsquos equation in CGS system is lsquoyenAacutenotAumlcedilAgravepoundiumlrsquopoundAgrave cedilAgravelaquoAumlAtildePAgravegAgravetordfAgravepoundAgraveAumlszlig CGS ordfAgravearingordfAgravecedilEacuteUumlAiAgraveAumldegegrave F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgraveAringzAgravegAgraveAvEacute

sectgEacuteAiAgraveAumlsectordmAgraveAumlzAgraveAuml (A) nabla

2 V = ndash 4πσ (B) nabla

2 V = ndash 4πρ

(C) nabla2 V = 0 (D) nabla

2 V = ndash

ρ

ε0

31 Maxwellrsquos equations in free space are ordfAgraveAumlAumlPAgraveUcirc cedilAgraveUumlfrac14AgravezAgravedegegrave ordfAgraveiAacutearingPiumligraveordfEacute5iumlpoundAgrave cedilAgravelaquoAumlAtildePAgravegAgravetUAgravefrac14AgraveAuml F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgraveAringzAgravegAgraveAvEacute EgAgraveAumlvAgraveUcirczEacute

(A) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J + micro0 ε0 part

rarr

E

partt

(B) nabla rarr

E = 0 nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt

(C) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J

(D) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt


Physics 11

32 Boundary conditions on fields at the interface between the two different media and having no free charge carriers at the interface are

JgAgraveqAgraveAuml laquocopyuumlpoundAgraveszlig ordfAgraveiAacutezsAgravearingordfAgraveAumlUAgravefrac14Agrave poundAgraveqAgraveAumllaquopoundAgrave CAvAgravegiuml cedilAgraveAyenAgravePAgraveethzAgravedegegravepoundAgrave PEacuteeumlAtildevAgraveaeligUAgravefrac14Agrave ordfEacuteAumlAtildedegpoundAgrave ordfAgraveAumlvAgraveAumlUcirc CAvAgravegiuml cedilAgraveAyenAgravePAgraveethzAgravedegegrave AiAgraveiAacuteordfAgraveAringzEacuteAtilde ordfAgraveAumlAumlPAgraveUcirc laquozAgraveAumlaringviuml yenAgraveAEliggAgravet ordfAacuteordmAgravePAgraveUAgravefrac14AgraveAuml EregegravezAgrave sup1AtildeordfAgraveiAacute sup1UumlwUAgravefrac14AgraveAuml F ordfAgraveAumlAumlAcentpoundAgraveAwgAgraveAumlvAgraveUcirczEacute

(A) 0Bmicro

1B

micro

1and 0EE0BBσDD ||

22

||1

1

||2

||121f21 =minus=minus=minus=minus

perpperpperpperp

(B) 0B

micro

1B

micro

1and

t

BEE0BB0DD ||

22

||1

1

||2

||12121 =minus

part

partminus=minus=minus=minus

perpperpperpperp

(C) 0B

micro

1B

micro

1and 0EE0BB0EεEε ||

22

||1

1

||2

||1212211 =minus=minus=minus=minus

perpperpperpperp

(D) 0B

micro

1B

micro

1and 0EE0BB0DD ||

22

||1

1

||2


perpperpperpperp

33 A static magnetic field at a point lsquorrsquo can be derived from a scalar potential

(A) If the current density is zero at that point

(B) If the current density is zero everywhere

(C) If L 0dlB =

r for the closed path L

(D) None of these

copyAzAgraveAuml lsquorrsquopoundAgravedegegrave MAzAgraveAuml cedilAacuteUumlnotAuml PAacuteAvAgravePEacuteeumlAtildevAgraveaeligordfAgravepoundAgraveAumlszlig CcentplusmnAgrave laquo sAgraveordfAgravecentAzAgrave F ordfAgraveAumlAumlAcentpoundAgrave AiAgraveiAacuteordfAgrave cedilAgraveAzAgrave sAgraveethzAgravedegegrave yenAgraveqEacuteAiAgraveAumlsectordmAgraveAumlzAacuteVzEacute

(A) copyAzAgraveAumllaquopoundAgravedegegrave laquozAgraveAumlaringvAgraveagraveccedilordfAacuteordmAgravezAgrave cedilAacuteAzAgraveaeligvEacuteAiAgraveAumlAuml plusmnAgraveAEligpoundAgravearingordfAacuteVzAgraveYacutegEacute

(B) J5Aacuteegrave PAgraveqEacuteUAgravefrac14Agravedegegrave laquozAgraveAumlaringvAgraveagraveccedilordfAacuteordmAgravezAgrave cedilAacuteAzAgraveaeligvEacuteAiAgraveAumlAuml plusmnAgraveAEligpoundAgravearingordfAacuteVzAgraveYacutegEacute

(C) cedilAgraveAordfAgraveEgravevAgrave yenAgravexAgrave L UEacute L 0dlB =

r DVzAgraveYacutegEacute

(D) ordfEacuteAumlAtildedegpoundAgrave AiAgraveiAacuteordfAgraveAringzAgraveAElig Cregegrave


12 Physics

34 An electromagnetic wave is travelling normally from a non-conducting linear medium (1) to a perfectly conducting medium (2) Then the wave is

(A) Totally transmitted to the medium 2 with same phase (B) Totally reflected back to the medium 1 with the same phase

(C) Totally reflected back to the medium 1 with a phase shift of 180deg

(D) Totally transmitted to the medium 2 with a phase shift of 180deg MAzAgraveAuml laquozAgraveAumlaringvAacuteIgraveAwAtildeAiAgraveAuml vAgravegAgraveAUAgraveordfAgraveAring CordfAacuteordmAgravePAgrave gEacuteAtildeTAtildeAiAgraveAuml ordfAgraveiAacutezsAgravearingordfAgraveAuml 1 ordfAgraveAumlvAgraveAumlUcirc yenAgravejyenAgraveAEligteth

ordfAacuteordmAgravePAgrave ordfAgraveiAacutezsAgravearingordfAgraveAuml 2 gAgrave poundAgraveqAgraveAumllaquopoundAgrave sup1AtildeordfEacuteAumlAiAgraveAuml ordfEacuteAumlAtilde5Eacute MAzAgraveAuml cedilAacuteordfAgraveiAacutepoundAgravearing DyenAacutevAgraveordfAgravepoundAgraveAumlszligAlAuml ordfAgraveiAacuterzAgravegEacute DUAgrave laquozAgraveAumlaringvAacuteIgraveAwAtildeAiAgraveAuml vAgravegAgraveAUAgraveordfAgraveAring F ordfAgraveAumlAumlAcentpoundAgravezAacuteVgAgraveAumlvAgraveUcirczEacute

(A) ordfAgraveiAacutezsAgravearingordfAgraveAuml 2PEacuteIgrave CzEacuteAtilde CordfAgravecedilEacuteUumlAiAgraveAumldegegrave MmAacuteOumlgEacuteAiAgraveiAacuteV yenAgraveaeligcedilAgravegAgravetordfAacuteVgAgraveAumlvAgraveUcirczEacute (B) ordfAgraveiAacutezsAgravearingordfAgraveAuml 1PEacuteIgrave CzEacuteAtilde CordfAgravecedilEacuteUumlAiAgraveAumldegegrave MmAacuteOumlgEacute raquoordfAgraveAumlAumlaumlRordfAacuteV yenAgraveaeligwyensAgraveregpoundAgraveUEacuteAEligArgAgraveAumlvAgraveUcirczEacute (C) ordfAgraveiAacutezsAgravearingordfAgraveAuml 1PEacuteIgrave 180deg PEacuteAEligAtildepoundAgravezAgrave CordfAgravecedilEacuteUumlAiAgraveAuml ordmEacuteAEliggAgraveUEacute MmAacuteOumlgEacuteAiAgraveiAacuteV raquoordfAgraveAumlAumlaumlRordfAacuteV

yenAgraveaeligwyensAgraveregpoundAgraveUEacuteAEligArgAgraveAumlvAgraveUcirczEacute (D) ordfAgraveiAacutezsAgravearingordfAgraveAuml 2PEacuteIgrave 180deg PEacuteAEligAtildepoundAgravezAgrave CordfAgravecedilEacuteUumlAiAgraveAuml ordmEacuteAEliggAgraveUEacute MmAacuteOumlgEacuteAiAgraveiAacuteV yenAgraveaelig AgravegAgravetordfAacuteVgAgraveAumlvAgraveUcirczEacute

35 If rarr

n

is the polarization vector and rarr

k

is the direction of propagation of plane electromagnetic wave then

rarr

n zAgraveEgravelaquoAtildePAgravegAgravet cedilAgravecentplusmnAgraveordfAacuteVzAgraveAumlYacute ordfAgraveAumlvAgraveAumlUcirc rarr

k AiAgraveAumlAuml cedilAgraveordfAgraveAumlvAgravereg laquozAgraveAumlaringvAacuteIgraveAwAtildeAiAgraveAuml vAgravegAgraveAUAgravezAgrave yenAgraveaeligcedilAgravegAgraveuEacuteAiAgraveAuml centPAacuteIgraveVzAgraveYacutegEacute DUAgrave

rarr

n = rarr

k (B) rarr

n = ndash rarr

k

(C) rarr

n rarr

k = 0 (D) rarr

n times rarr

k = 0

36 The power radiated by an oscillating magnetic dipole is (A) Proportional to the square of frequency of oscillation (B) Inversely proportional to the square of frequency of oscillation (C) Proportional to the fourth power of the frequency of oscillation (D) Inversely proportional to the fourth power of the frequency of oscillation MAzAgraveAuml DAzEacuteAEligAtilderegPAgrave PAacuteAwAtildeAiAgraveAuml centeacute-zsAgraveAumlaeligordfAgravecentAzAgrave laquoQgAgravetAcirccedilAgraveAumlordfAgrave cedilAacuteordfAgraveAumlxAgraveetharingordfAgraveAring (A) DAzEacuteAEligAtilderegpoundAgrave DordfAgravevAacuteethAPAgravezAgrave ordfAgraveUAgraveethPEacuteIgrave CpoundAgraveAumlyenAacutevAgraveordfAacuteVgAgraveAumlvAgraveUcirczEacute (B) DAzEacuteAEligAtilderegpoundAgrave DordfAgravevAacuteethAPAgravezAgrave ordfAgraveUAgraveethPEacuteIgrave laquo5EacuteAEligAtildeordfAgraveiAacutepoundAgraveAumlyenAacutevAgraveordfAacuteVgAgraveAumlvAgraveUcirczEacute (C) DordfAgravevAacuteethAPAgrave DAzEacuteAEligAtilderegpoundAgravezAgrave poundAacuteregIgravepoundEacuteAtilde WAacutevAgravePEacuteIgrave CpoundAgraveAumlyenAacutevAgraveordfAacuteVgAgraveAumlvAgraveUcirczEacute (D) DordfAgravevAacuteethAPAgrave DAzEacuteAEligAtilderegpoundAgravezAgrave poundAacuteregIgravepoundEacuteAtilde WAacutevAgravePEacuteIgrave laquo5EacuteAEligAtildeordfAgraveiAacutepoundAgraveAumlyenAacutevAgraveordfAacuteVgAgraveAumlvAgraveUcirczEacute


Physics 13

37 The energy stored in an electromagnetic field per unit volume is

yenAgraveaeligw WAgravelPAgrave UAacutevAgraveaeligPEacuteIgrave laquozAgraveAumlaringvAacuteIgraveAwAtildeAiAgraveAuml PEacuteeumlAtildevAgraveaeligzAgravedegegrave plusmnEacuteAtildeRgAgraveuEacuteUEacuteAEligArgAgraveAumlordfAgrave plusmnAgraveQUcircAiAgraveAumlAuml

(A) Bmicro

1 Eε

00

rr+ (B) B E

micro

ε

0

0rr

sdot

(C) 22

0

0 B E 2micro

εsdot (D)

+

2

0

20 B

micro

1Eε

2

1

38 If the output of a transistor should be proportional to the input signal the operating point should be

(A) In the saturation region (B) In the cutoff region

(C) In the active region (D) Anywhere

mAacuteaeligcurrenigravecedilAgraveOumlgiumlpoundAgrave GvAgraveagravepoundAgraveszligordfAgraveAring ordmAgraveAEligrPEacute sup1UAgraveszlig5iumlUEacute CpoundAgraveAumlyenAacutevAgraveordfAacuteVgAgraveumlEacuteAtildePEacuteAzAgravegEacute PAacuteAiAgraveiAacuteethZAgravegAgravet copyAzAgraveAuml F ordfAgraveAumlAumlAcentpoundAgrave AiAgraveiAacuteordfAgraveAringzAacuteVgAgraveAumlvAgraveUcirczEacute

(A) cedilAgraveAvAgraveEgraveyenAgraveUcirc ordfAgraveregAiAgraveAuml (B) PAgravemiuml-Dyensiuml ordfAgraveregAiAgraveAuml

(C) QaeligAiAgraveiAacutesup2Atildereg ordfAgraveregAiAgraveAuml (D) J5AacuteegravezAgravegAgraveAElig

39 In a p-type semiconductor the minority carriers are

(A) Holes (B) Electrons

(C) Impurity atoms (D) Phonons

MAzAgraveAuml p-ordfAgraveiAacutezAgravej CgEacuteordfAacuteordmAgravePAgravezAgravedegegrave CregagravecedilAgraveASAacutearing ordfAacuteordmAgravePAgraveUAgravefrac14AgraveAuml AiAgraveiAacuteordfAgraveAringordfEacuteAzAgravegEacute

(A) gAgraveAzsAgraveaeligUAgravefrac14AgraveAuml (B) J5EacutePAacuteOumlccedilpoundiumlUAgravefrac14AgraveAuml

(C) PAgraveregaumlplusmnAgrave yenAgravegAgraveordfAgraveiAacutetAumlUAgravefrac14AgraveAuml (D) yensEacuteAEligAtildepoundAacutepoundiumlUAgravefrac14AgraveAuml

40 A piezoelectric crystal can be used as transducer for measurement of

(A) temperature (B) pressure

(C) voltage (D) current

brvbargEacutehAEligAtildeJ5EacuteQOumlccedilPiuml cedilAgraveagravenPAgraveordfAgravepoundAgraveAumlszlig F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgraveAringzAgravegAgrave ordfAgraveiAacuteyenAgravepoundEacuteUAacuteV mAacuteaeligpoundiumligraveqAgraveAEligaringcedilAgravegiuml DV sectfrac14AgravecedilAgravesectordmAgraveAumlzAgraveAuml

(A) GmicroAgraveUacutevEacute (B) MvAgraveUcircqAgrave

(C) ordfEacuteCcedilAtilde5EacuteOumlAtildeeiuml (D) PAgravegEacuteAmiuml


14 Physics

41 Which one of the following is the advantage of using single sideband transmission

(A) Increases reliability (B) Small bandwidth

(C) Easy to demodulate (D) Easy to transmit without errors

KPAgrave cedilEacuteEcircqiumlumlAacutearingAqiuml yenAgraveaeligcedilAgravegAgraveuEacuteAiAgraveAuml GyenAgraveAiEacuteAEligAtildeUAgraveAacutemicroaring sectOgraveAacutemicroaringecirc ƒAumlaringecircrsquoaringeumlNtildefrac14ethsup2igravearingecircecirc hellipOcircaringiacuteuacute˜microaringacircyumlaringNtildendashOacute sup2igravearingigraveaeligOcircaringiacuteuacuteAacutemicroaringecirc

(A) poundAgraveAcopyPAacuteordmAgraveethvEacuteAiAgraveAumlpoundAgraveAumlszlig ordmEacuteaNtildecedilAgraveAumlvAgraveUcirczEacute

(B) PAgraverordfEacuteAuml vAgravegAgraveAUAgrave laquocedilAacuteUcircgAgraveordfAgravepoundAgraveAumlszlig sectfrac14AgravecedilAgraveAumlvAgraveUcirczEacute

(C) yenAgraveaeligvAacutearingfrac14AgraveordfAgravercedilAgraveregAuml cedilAgraveAumlreg sAgraveordfAacuteVzEacute

(D) zEacuteAEligAtildemicroAgraveUAgravefrac12regegravezEacute yenAgraveaeligcedilAgravegAgravetAcirccedilAgraveregAuml cedilAgraveAumlreg sAgraveordfAacuteVzEacute

42 What is the full scale output voltage of a 6-bit binary ladder if lsquo0rsquo= 0 V and lsquo1rsquo = + 10 V

lsquo0rsquo = 0 V ordfAgraveAumlvAgraveAumlUcirc lsquo1rsquo = + 10 V DzAgravegEacute 6-copymiuml centeacuteordfAgraveiAacutepoundAgrave 5AacutearingqAgravegiumlpoundAgrave yenAgraveAEligteth yenAgraveaeligordfAgraveiAacutetzAgrave GvAacuteagravecentvAgrave ordfEacuteCcedilAtilde5EacuteOumlAtildeeiuml F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgraveAringzAacuteVzEacute

(A) (63 times 10)64 V (B) 1064 V

(C) 10 V (D) 64 V

43 A molecule in the triplet state has a net electron spin of

waeligordfAgravefrac12 CordfAgravecedilEacuteUumlAiAgraveAumldegegrave MAzAgraveAuml CtAumlordfAgraveAring F PEacutefrac14Agrave˜tradepoundAgravemicroAgraveAumlOuml currenordfAgraveeacutefrac14Agrave J5EacutePAacuteOumlccedilpoundiuml sAgraveaeligordfAgraveAumltordfAgravepoundAgraveAumlszlig ordmEacuteAEligAcentgAgraveAumlvAgraveUcirczEacute

(A) 3 (B) 1

(C) 0 (D) frac12

44 Stokes lines in the Raman spectrum have

(A) longer wavelengths and higher intensity than anti Stokersquos lines

(B) shorter wavelengths and lower intensity than anti Stokersquos lines

(C) longer wavelengths and lower intensity than anti Stokersquos lines

(D) shorter wavelengths and higher intensity than anti Stokersquos lines gAacuteordfAgraveAumlpoundiuml gEacuteAEligAtilderaquovAgravezAgravedegegrave cedilEacuteAEligOumlAtildePiuml 5EacuteEcircpoundiumlUAgravefrac14AgraveAuml F PEacutefrac14AgraveVpoundAgravezAacuteYacuteVgAgraveAumlvAgraveUcirczEacute

(A) DaringAn cedilEacuteAEligOumlAtildePiuml 5EacuteEcircpoundiumlUAgravefrac12VAvAgrave GzAgraveYacutezAgrave vAgravegAgraveAUAacuteAvAgravegAgraveUAgravefrac14AgraveAuml ordfAgraveAumlvAgraveAumlUcirc ordmEacuteaNtildepoundAgrave wAtildeordfAgraveaeligvEacute

(B) DaringAn cedilEacuteAEligOumlAtildePiuml 5EacuteEcircpoundiumlUAgravefrac12VAvAgrave aPAgraveIgrave vAgravegAgraveAUAacuteAvAgravegAgraveUAgravefrac14AgraveAuml ordfAgraveAumlvAgraveAumlUcirc PAgraverordfEacuteAuml wAtildeordfAgraveaeligvEacute

(C) DaringAn cedilEacuteAEligOumlAtildePiuml 5EacuteEcircpoundiumlUAgravefrac12VAvAgrave GzAgraveYacutezAgrave vAgravegAgraveAUAacuteAvAgravegAgraveUAgravefrac14AgraveAuml ordfAgraveAumlvAgraveAumlUcirc PAgraverordfEacuteAuml wAtildeordfAgraveaeligvEacute

(D) DaringAn cedilEacuteAEligOumlAtildePiuml 5EacuteEcircpoundiumlUAgravefrac12VAvAgrave aPAgraveIgrave vAgravegAgraveAUAacuteAvAgravegAgraveUAgravefrac14AgraveAuml ordfAgraveAumlvAgraveAumlUcirc ordmEacuteaNtildepoundAgrave wAtildeordfAgraveaeligvEacute


Physics 15

45 Natural broadening of spectral lines is associated with (A) collision between atoms (B) magnetic interaction between atoms (C) finite lifetime of the energy states (D) velocity distribution of emitting atoms gEacuteAEligAtilderaquovAgrave gEacuteAtildeSEacuteUAgravefrac14Agrave cedilAacuteeacute sAacutelaquoPAgrave laquocedilAacuteUcircgAgraveordfAacuteUAgraveAumllaquoPEacute F PEacutefrac14AgraveVpoundAgraveordfAgraveAringzAgravePEacuteIgrave cedilAgraveAsectAcentuumlsup1zEacute (A) yenAgravegAgraveordfAgraveiAacutetAumlUAgravefrac14Agrave poundAgraveqAgraveAumllaquopoundAgrave cedilAgraveAWAgravemicroAgraveethuEacute (B) yenAgravegAgraveordfAgraveiAacutetAumlUAgravefrac14Agrave poundAgraveqAgraveAumllaquopoundAgrave PAacuteAwAtildeAiAgraveAuml CAvAgravegAgraveQaeligAiEacuteAuml (C) plusmnAgraveQUcirc sup1UumlwUAgravefrac14Agrave yenAgravejlaquoAumlvAgrave fAtildeordfAacuteordfAgravecentuuml (D) yenAgravegAgraveordfAgraveiAacutetAumlUAgravefrac14Agrave GvAgraveigravefethcedilAgraveAumlordfAgrave ordfEacuteAtildeUAgravezAgrave laquovAgravegAgraveuEacute

46 Light emission from ordinary optical sources is incoherent because (A) emission is predominantly spontaneous (B) emission is predominantly stimulated (C) emission occurs at several wavelengths (D) emission occurs with low intensity cedilAacuteordfAgraveiAacutepoundAgravearing zAgraveAumlaringw DPAgravegAgraveUAgravefrac12AzAacuteUAgraveAumlordfAgrave umlEacutefrac14AgraveQpoundAgrave GvAgraveigravedethpoundEacuteAiAgraveAumlAuml EpoundiumlPEacuteAEligordmEacutegEacuteAmiuml DVgAgraveAumlvAgraveUcirczEacute

KPEacuteAzAgravegEacute GvAgraveigravedethpoundEacuteAiAgraveAumlAuml (A) yenAgraveaeligzsAacutepoundAgraveordfAacuteV cedilAacuteeacute sAacutelaquoPAgraveordfAacuteVgAgraveAumlvAgraveUcirczEacute (B) yenAgraveaeligzsAacutepoundAgraveordfAacuteV ZEacuteAEligAtildecentvAgraveordfAacuteVgAgraveAumlvAgraveUcirczEacute (C) CpoundEacuteAtildePAgrave vAgravegAgraveAUAacuteAvAgravegAgraveUAgravefrac14Agravedegegrave cedilAgraveA sAgravelaquocedilAgraveAumlvAgraveUcirczEacute (D) PAgraverordfEacuteAuml wAtildeordfAgraveaeligvEacuteAiAgraveAumldegegrave cedilAgraveA sAgravelaquocedilAgraveAumlvAgraveUcirczEacute

47 For a cavity of length 50 cm the frequency separation between axial modes is 50 cedilEacuteAlaquoAumlAtilde GzAgraveYacutezAgrave PAacutearinglaquon CQeumlAtildeAiAgraveAuml ordfAgraveiAacuteUAgraveethUAgravefrac14Agrave poundAgraveqAgraveAumllaquopoundAgrave DordfAgravevAacuteethAPAgrave umlEacuteAtildeyenAgraveethrcedilAgraveAumllaquoPEacuteAiAgraveAumlAuml

F PEacutefrac14AgraveVpoundAgraveparaOumlgAgraveAumlvAgraveUcirczEacute (A) 100 kHz (B) 300 kHz (C) 300 MHz (D) 1 MHz

48 Lifetime of a metastable state involved in lasting action is of the order of (A) seconds (B) microseconds (C) milliseconds (D) nanoseconds 5EacuteAtildecedilAgravegiuml (frac14aring microethsup2igravearingecircecircOcircaring) QaeligAiEacuteAumlAiAgraveAumldegegrave Mfrac14AgraveUEacuteAEligArgAgraveAumlordfAgrave ordfEacuteAumlmAacute sup1UumlgAgravesup1UumlwAiAgraveAuml fAtildeordfAacuteordfAgravecentuumlAiAgraveAumlAuml F

PEacutefrac14AgraveVpoundAgraveparaOumlgAgraveAumlvAgraveUcirczEacute (A) cedilEacutePEacuteAqAgraveAumlUAgravefrac14AgraveAuml (B) ordfEacuteAumlEcircPEacuteAEligaeligAtilde cedilEacutePEacuteAqAgraveAumlUAgravefrac14AgraveAuml (C) laquoAumldeg cedilEacutePEacuteAqAgraveAumlUAgravefrac14AgraveAuml (D) poundAacutearingpoundEacuteAEligAtilde cedilEacutePEacuteAqAgraveAumlUAgravefrac14AgraveAuml


16 Physics

49 Transitions between high n states of Hydrogen are observed in space In which part of the electromagnetic spectrum will the transition between n = 110 and n = 109 designated as 109 α be seen (Rydberg constant R = 10967758 cmndash1)

(A) Ultraviolet region (B) X-ray region (C) Far infrared region (D) Centimetre wavelength radio region dregdpoundAgravePAgravezAgrave ordmEacuteaNtildepoundAgrave n sup1UumlwUAgravefrac14Agrave poundAgraveqAgraveAumllaquopoundAgrave cedilAgraveAPAgraveaeligordfAgraveAumltUAgravefrac14AgravepoundAgraveAumlszlig umlAacuteordmAacutearingPAacuteplusmnAgravezAgravedegegrave UAgraveordfAgraveAumlcurrencedilAgrave5AacuteUAgraveAumlvAgraveUcirczEacute

ordmAacuteUAacutezAgravegEacute laquozAgraveAumlaringvAacuteIgraveAwAtildeAiAgraveAuml gEacuteAEligAtilderaquovAgravezAgrave AiAgraveiAacuteordfAgrave sAacuteUAgravezAgravedegegrave 109α JAzAgraveAuml ordmEacutecedilAgravejsup1gAgraveAumlordfAgrave n = 110 ordfAgraveAumlvAgraveAumlUcirc n = 109 poundAgrave poundAgraveqAgraveAumllaquopoundAgrave cedilAgraveAPAgraveaeligordfAgraveAumltordfAgravepoundAgraveAumlszlig PAacutetsectordmAgraveAumlzAgraveAuml (jqAgraveacircUiumleth PAacutepoundiumligravecedilEacuteOumlAmiuml R = 10967758 cmndash1)

(A) CwpoundEacuteAtildegAgravefrac14Eacute ordfAgraveregAiAgraveAuml (B) PAgraveeuml-QgAgravet ordfAgraveregAiAgraveAuml (C) CordfAgravePEacuteAyenAgraveAuml ordfAgraveregAiAgraveAuml (D) gEacuteAtilderAiEacuteAEligAtilde vAgravegAgraveAUAacuteAvAgravegAgrave ordfAgraveregAiAgraveAuml

50 A system comprises of two spin frac12 particles If the system has a total spin angular momentum of zero then what is the probability of finding both particles with spin up

MAzAgraveAuml ordfAgravearingordfAgravecedilEacuteUumlAiAgraveAumldegegrave frac12 sAgraveaeligordfAgraveAumltlaquogAgraveAumlordfAgrave JgAgraveqAgraveAuml PAgravetUAgravefrac12ordfEacute ordfAgravearingordfAgravecedilEacuteUumlAiAgraveAuml MlAumlOuml sAgraveaeligordfAgraveAumlt PEacuteAEligcurrenAtildeAiAgraveAuml cedilAgraveAordfEacuteAtildeUAgraveordfAgraveAring plusmnAgraveAEligpoundAgravearingordfAacuteVzAacuteYacuteUAgrave ordfEacuteAumlAtilderegAumlaumlR sAgraveaeligordfAgraveAumltvEacuteAiEacuteAEligAcentUEacute JgAgraveqAgraveAuml PAgravetUAgravefrac14AgravepoundAgraveAumlszlig PAgraveAqAgraveAumlraquorAiAgraveAumlAumlordfAgrave cedilAgraveA sAgraveordfAgravecurrenAtildeAiAgraveAumlvEacuteAiAgraveAumlAuml

(A) 1 (B) 050 (C) 025 (D) 0

51 The energy eigen values of the quantum linear harmonic oscillator are given by En Which

one of the following statements is not true (A) The separation between the energy levels increases as n increases (B) The quantum linear harmonic oscillator approaches the classical harmonic

oscillator for very large n (C) The ground state energy is non zero (D) The expectation value of the kinetic energy is the same as the expectation

value of the potential energy in any state PAacuteeacuteAlordfAgraveiiuml gEacuteAtildeTAiAgraveAuml cedilAgraveAUAgravevAgrave DAzEacuteAEligAtilderegPAgravezAgrave LUAgravepoundiuml plusmnAgraveQUcirc ordfAgraveiEumlregaringUAgravefrac14AgraveAuml En DVgAgraveAumlvAgraveUcirczEacute

ordmAacuteVzAacuteYacuteUAgrave F PEacutefrac14AgravePAgraveAqAgrave AiAgraveiAacuteordfAgrave ordmEacuteAtildefrac12PEacuteAiAgraveAumlAuml cedilAgravejAiAgraveiAacuteVgAgraveAumlordfAgraveAringcentregegrave (A) n ordmEacuteZAacuteNtildezAgraveAvEacute plusmnAgraveQUcircAiAgraveAuml ordfAgraveAumllOumlUAgravefrac14AgravedegegravepoundAgrave laquoAUAgraveqAgraveuEacuteAiAgraveAumlAuml ordmEacuteZAacuteNtildeUAgraveAumlvAgraveUcirczEacute (B) PAacuteeacuteAlordfAgraveiiuml gEacuteAtildeTAiAgraveAuml cedilAgraveAUAgravevAgrave DAzEacuteAEligAtilderegPAgraveordfAgraveAring CwAtilde zEacuteAEligqAgraveOslash n UAacuteV PAacuteegravesup1PAgrave5iuml

cedilAgraveAUAgravevAgrave DAzEacuteAEligAtilderegPAgraveordfAgravepoundAgraveAumlszlig cedilAgraveAcentuumlcedilAgraveAumlvAgraveUcirczEacute (C) plusmnAgraveQUcircAiAgraveAuml vAgravefrac14AgraveordfAgraveAumllOumlzAgrave sup1UumlwAiAgraveAumlAuml plusmnAgraveAEligpoundAgravearingordfAacuteVgAgraveAumlordfAgraveAringcentregegrave (D) AiAgraveiAacuteordfAgraveAringzEacuteAtilde sup1UumlwAiAgraveAumldegegrave ZAgraveregpoundAgraveplusmnAgraveQUcircAiAgraveAuml currenjAtildeQeumlvAgrave ordfAgraveiEumlregaringordfAgraveAring laquo sAgraveordfAgrave plusmnAgraveQUcircAiAgraveAuml currenjAtildeQeumlvAgrave

ordfAgraveiEumlregaringzAgraveAvEacuteAiEacuteAumlAtilde EgAgraveAumlvAgraveUcirczEacute


Physics 17

52 Simultaneous precise measurement of two dynamic variables is possible only if the operators associated with them

(A) commute individually with the Hamiltonian (B) are transposed conjugates (adjoints) of each other (C) commute with each other (D) Cannot say as it depends on the particular operators JgAgraveqAgraveAuml UAgravewsup2Atildereg ZAgravegAgraveUAgravefrac14Agrave KPAgravePAacutedegPAgrave RavAgraveordfAacutezAgrave ordfAgraveiAacuteyenAgravepoundEacuteAiAgraveAumlAuml CordfAgraveAringUAgravefrac14EacuteAEligAcentUEacute

cedilAgraveordmAgraveordfAgravevAgraveethpoundEacuteUEacuteAEligArgAgraveAumlordfAgrave DyenAgravegEacuteAtildelgiumlUAgravefrac14AgraveAuml F PEacutefrac14AgraveVpoundAgraveAwzAacuteYacuteUAgrave ordfAgraveiAacutevAgraveaelig cedilAacutezsAgravearingordfAacuteUAgraveAumlvAgraveUcirczEacute (A) ordmAacutearinglaquoAuml5EacuteAEligOumlcurrenAiEacuteAumlpoundiumlpoundEacuteAEligAcentUEacute cedilAgraveeacutevAgraveAvAgraveaeligordfAacuteV yenAgravejordfAgravewethsup1zAacuteUAgrave (B) MAzAgravePEacuteAEligIgraveAzAgraveAuml laquoyenAgraveAiAgraveiAacuteethAiAgraveAuml CpoundAgraveAumlordfAgravewethUAgravefrac14AacuteVzAgraveYacutegEacute (C) MAzAgravePEacuteAEligIgraveAzAgraveAuml yenAgravejordfAgravewethsup1zAacuteUAgrave (D) AringAacutetradecurrenUacuteEgravearingplusmn DyenAgravegEacuteAtildelsup2microoacuteTHORN ordfEacuteAumlAtilde5Eacute CordfAgraveregAcopyvAgraveordfAacuteVgAgraveAumlvAgraveUcirczEacute ŠAumlaringecircAEligOcircaringOgravefrac12NtildeOacute

53 Diracrsquos relativistic theory predicts the existence of the (A) electron (B) positron (C) proton (D) neutron lsquorgAacutePiumlrsquopoundAgrave cedilAacuteyenEacuteAtildePAgraveeumlvAacutevAgraveaumlPAgrave sup1zAacuteTHORNAvAgraveordfAgraveAring F PEacutefrac14AgravePAgraveAqAgrave AiAgraveiAacuteordfAgraveAringzAgravegAgrave EgAgraveAumllaquoPEacuteAiAgraveAumlpoundAgraveAumlszlig HraquocedilAgraveAumlvAgraveUcirczEacute (A) J5EacutePAacuteOumlccedilpoundiuml (B) yenAacutesup1mAacuteaeligpoundiuml (C) yenEacuteAEligaeligAtildemAacutepoundiuml (D) poundAgraveAEligaringmAacuteaeligpoundiuml

54 The wavefunction of a particle trapped in space between x = 0 and x = L is given by

L

)sin(2πA)(ψ

xx = where A is a constant The probability of finding the particle is

maximum when x is lsquoArsquo AiAgraveAumlAuml sup1UumlgAacuteAPAgraveordfAacuteVgAgraveAumlordfAgrave x = 0 ordfAgraveAumlvAgraveAumlUcirc x = L UAgravefrac14Agrave poundAgraveqAgraveAumllaquopoundAgrave eAacuteUAgravezAgravedegegrave sup1regAumlQgAgraveAumlordfAgrave PAgravetzAgrave

vAgravegAgraveAUAgrave yensAgraveregpoundAgraveordfAgraveAring L

)sin(2πA)(ψ

xx = centAzAgrave currenAtildeqAgraveregagravenOumlzEacute ordmAacuteVzAgraveYacutegEacute lsquoxrsquo F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgrave

ordfAgraveiEumlregaringordfAgravepoundAgraveAumlszlig ordmEacuteAEligAcentzAacuteUAgrave PAgravetordfAgravepoundAgraveAumlszlig PAgraveAqAgraveAumlraquorAiAgraveAumlAumlordfAgrave cedilAgraveA sAgraveordfAgravecurrenAtildeAiAgraveAumlvEacute ordmEacuteZAacuteNtildeVgAgraveAumlvAgraveUcirczEacute (A) L4 (B) L2 (C) L6 and L3 (D) L4 and 3L4

55 The relation between the principal quantum number n and energy of the Hydrogen atom is given by

yenAgraveaeligzsAacutepoundAgrave PAacuteeacuteAlordfAgraveiiuml cedilAgraveASEacutearing n ordfAgraveAumlvAgraveAumlUcirc dregdpoundAgravePAgravezAgrave yenAgravegAgraveordfAgraveiAacutetAumllaquopoundAgrave plusmnAgraveQUcircAiAgraveAuml poundAgraveqAgraveAumllaquopoundAgrave cedilAgraveAsectAzsAgraveordfAgravepoundAgraveAumlszlig F PEacutefrac14AgravePAgraveAqAgrave AiAgraveiAacuteordfAgrave cedilAgravelaquoAumlAtildePAgravegAgravetordfAgraveAring cedilAgraveAEligacedilAgraveAumlvAgraveUcirczEacute

(A) En prop 1n2 (B) En prop ndash1n2

(C) En prop n2 (D) En prop ndash n2


18 Physics

56 A quantum particle of mass m is constrained to remain at a distance of r0 from the origin

If l is the orbital angular momentum quantum number then the possible energy values of the particle are given by

zAgraveaeligordfAgravearinggAacutesup2(m)CpoundAgraveAumlszlig ordmEacuteAEligAcentgAgraveAumlordfAgrave PAacuteeacuteAlordfAgraveiiuml PAgravetordfAgravepoundAgraveAumlszlig ordfAgraveAumlAEligregcedilAacuteUumlpoundAgravecentAzAgrave r0 poundAgrave CAvAgravegAgravezAgravedegegravegAgraveAumlordfAgraveAvEacute yenAgraveaeligwsectAcentuuml Agrave5AacuteVzEacute l EzAgraveAuml PAgravePAgraveeumlPAgrave PEacuteAEligcurrenAtildeAiAgraveAuml cedilAgraveAordfEacuteAtildeUAgravezAgrave PAacuteeacuteAlordfAgraveiiuml cedilAgraveASEacutearingAiAgraveiAacutezAgravegEacute DUAgrave PAgravetzAgrave cedilAgraveA sAacuteordfAgravearing plusmnAgraveQUcirc ordfAgraveiEumlregaringUAgravefrac14AgravepoundAgraveAumlszlig F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgrave cedilAgravelaquoAumlAtildePAgravegAgravetordfAgraveAring currenAtildeqAgraveAumlvAgraveUcirczEacute

(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20

57 A carbon nucleus emits a particle lsquoxrsquo and changes into nitrogen according to the equation

x+rarr NC14

7

14

6 Then lsquoxrsquo is

(A) A neutron (B) An electron (C) A proton (D) A photon

x+rarr NC14

7

14

6 cedilAgravelaquoAumlAtildePAgravegAgravetzAgrave yenAgraveaeligPAacutegAgrave MAzAgraveAuml PAacutesectethpoundiuml yenAgravegAgraveordfAgraveiAacutetAuml copyAtildedordfAgraveAring lsquoxrsquo

PAgravetUAgravefrac14AgravepoundAgraveAumlszlig GvAgraveigravefethUumlYacute UumlEgraveaeligsup2microaringbrvbarAumlaringrsquoaringOcircaelig˜trade EcircAacutemicroaringNtildendashUumlEgravearingecircfrac14aringfrac34Aacutemicroeth F cedilAgravelaquoAumlAtildePAgravegAgravetzAgravedegegrave lsquoxrsquo CAzAgravegEacuteAtildepoundAgraveAuml (A) poundAgraveAEligaringmAacuteaeligpoundiuml (B) J5EacutePAacuteOumlccedilpoundiuml (C) yenEacuteAEligaeligAtildemAacutepoundiuml (D) yensEacuteAEligAtildemAacutepoundiuml

58 Masses of two isobars 29Cu64 and 30Zn64 are 639298 amu and 639292 amu respectively

From this data one may infer that (A) 30Zn64 is radioactive decaying to 29Cu64 through gamma decay

(B) 29Cu64 is radioactive decaying to 30Zn64 through beta decay

(C) 29Cu64 is radioactive decaying to 30Zn64 through gamma decay

(D) 30Zn64 is radioactive decaying to 29Cu64 through alpha decay

29Cu64 ordfAgraveAumlvAgraveAumlUcirc 30Zn64 LcedilEacuteAEligAtildeumlAacutegiumlUAgravefrac14Agrave zAgraveaeligordfAgravearinggAacutesup2UAgravefrac14AgraveAuml CpoundAgraveAumlPAgraveaeligordfAgraveAumlordfAacuteV 639298 amu ordmAacuteUAgraveAElig 639292 amu EgAgraveAumlvAgraveUcircordfEacute F zAgravevAacuteUcircAplusmnAgravecentAzAgrave wfrac12AiAgraveAumlsectordmAgraveAumlzEacuteAtildepoundEacuteAzAgravegEacute

(A) 30Zn64 laquoQgAgravet yenAgravelAumlordfAacuteVzAgraveAumlYacute γminusPAgraveeumlAiAgraveAumlzAgrave ordfAgraveAumlAEligregPAgrave 29Cu64 UEacute QeumlAtildetAcirccedilAgraveAumlvAgraveUcirczEacute

(B) 29Cu64 laquoQgAgravet yenAgravelAumlordfAacuteVzAgraveAumlYacute βminusPAgraveeumlAiAgraveAumlzAgrave ordfAgraveAumlAEligregPAgrave 30Zn64 UEacute QeumlAtildetAcirccedilAgraveAumlvAgraveUcirczEacute

(C) 29Cu64 laquoQgAgravet yenAgravelAumlordfAacuteVzAgraveAumlYacute γminusPAgraveeumlAiAgraveAumlzAgrave ordfAgraveAumlAEligregPAgrave 30Zn64 UEacute QeumlAtildetAcirccedilAgraveAumlvAgraveUcirczEacute

(D) 30Zn64 laquoQgAgravet yenAgravelAumlordfAacuteVzAgraveAumlYacute αminusPAgraveeumlAiAgraveAumlzAgrave ordfAgraveAumlAEligregPAgrave 29Cu64 UEacute QeumlAtildetAcirccedilAgraveAumlvAgraveUcirczEacute


Physics 19

59 An alpha particle is equal to (A) Helium atom (B) An assembly of two protons and two neutrons (C) An assembly of two protons and two electrons (D) An assembly of two neutrons and two electrons

MAzAgraveAuml α PAgravetordfAgraveAring F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgraveAringzAgravePEacuteIgrave cedilAgraveordfAgraveAumlpoundAacuteVgAgraveAumlvAgraveUcirczEacute (A) raquoAtildedegAiAgraveAumlA yenAgravegAgraveordfAgraveiAacutetAuml (B) JgAgraveqAgraveAuml yenEacuteAEligaeligAtildemAacutepoundiuml ordfAgraveAumlvAgraveAumlUcirc JgAgraveqAgraveAuml poundAgraveAEligaringmAacuteaeligpoundiumlUAgravefrac14Agrave cedilAgraveordfAgraveAumlAEligordmAgrave (C) JgAgraveqAgraveAuml yenEacuteAEligaeligAtildemAacutepoundiuml ordfAgraveAumlvAgraveAumlUcirc JgAgraveqAgraveAuml J5EacutePAacuteOumlccedilpoundiumlUAgravefrac14Agrave cedilAgraveordfAgraveAumlAEligordmAgrave (D) JgAgraveqAgraveAuml poundAgraveAEligaringmAacuteaeligpoundiuml ordfAgraveAumlvAgraveAumlUcirc JgAgraveqAgraveAuml J5EacutePAacuteOumlccedilpoundiumlUAgravefrac14Agrave cedilAgraveordfAgraveAumlAEligordmAgrave 60 Scintillation counter works on the principle of (A) Compton effect (B) Photo multiplication (C) Fluorescence effect (D) Photoelectric effect sup1currenOuml5EacuteAtildemicroAgravepoundiuml UAgravetPAgraveordfAgraveAring F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgrave vAgravevAgraveeacutezAgrave DzsAacutegAgravezAgrave ordfEacuteAumlAtilde5Eacute PAacuteAiAgraveAumlethcurrenordfAgraveethraquocedilAgraveAumlvAgraveUcirczEacute (A) rsquoaeligETHAyenAgraveOumlpoundiuml yenAgravejuAacuteordfAgraveAuml (B) zAgraveAumlaringw ordfAgravecentuumlethcedilAgraveAumllaquoPEacute (C) yenAgraveaeligwcentAtildebrvbarUcirc yenAgravejuAacuteordfAgraveAuml (D) zAgraveAumlaringwlaquozAgraveAumlaringviuml yenAgravejuAacuteordfAgraveAuml 61 Liquid drop model will not explain the following (A) Radioactivity (B) Magic numbers (C) Atomic masses (D) Total energy of the nucleus zAgraveaeligordfAgrave ordmAgravecurren ordfAgraveiAacutezAgravejAiAgraveAumlAuml F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgraveAringzAgravepoundAgraveAumlszlig laquoordfAgravejcedilAgraveAumlordfAgraveAringcentregegrave (A) laquoQgAgravet yenAgravelAumlvAgraveeacute (B) ordfAgraveiAacutearingfPiuml cedilAgraveASEacutearingUAgravefrac14AgraveAuml (C) yenAgravegAgraveordfAgraveiAacutetAuml zAgraveaeligordfAgravearinggAacutesup2UAgravefrac14AgraveAuml (D) yenAgravegAgraveordfAgraveiAacutetAuml copyAtildedzAgrave MlAumlOuml plusmnAgraveQUcirc 62 The amount of energy released per unit mass is (A) More in nuclear fission than in nuclear fusion reaction (B) Less in nuclear fission than in nuclear fusion reaction (C) Equal in both nuclear fission and nuclear fusion reaction (D) None of the above yenAgraveaeligw WAgravelPAgrave zAgraveaeligordfAgravearinggAacutesup2AiAgraveAumlAuml copyqAgraveAumlUAgraveqEacuteUEacuteAEligfrac12cedilAgraveAumlordfAgrave plusmnAgraveQUcircAiAgraveAuml yenAgraveaeligordfAgraveiAacutetordfAgraveAring (A) copyAtilded cedilAgravelaquoAumlaumlregpoundAgrave yenAgraveaeligQaeligAiEacuteAumlVAvAgrave copyAtilded laquozAgravefrac14AgravepoundAgravezAgravedegegrave ordmEacuteZAacuteNtildeVgAgraveAumlvAgraveUcirczEacute (B) copyAtilded cedilAgravelaquoAumlaumlregpoundAgrave yenAgraveaeligQaeligAiEacuteAumlVAvAgrave copyAtilded laquozAgravefrac14AgravepoundAgravezAgravedegegrave PAgraverordfEacuteAumlAiAgraveiAacuteVgAgraveAumlvAgraveUcirczEacute (C) copyAtilded laquozAgravefrac14AgravepoundAgrave ordmAacuteUAgraveAElig copyAtilded cedilAgravelaquoAumlaumlregpoundAgrave yenAgraveaeligQaeligAiEacuteAumlUAgravefrac14EacutegAgraveqAgraveregAEligegrave cedilAgraveordfAgraveAumlpoundAacuteVgAgraveAumlvAgraveUcirczEacute (D) ordfEacuteAumlAtildedegpoundAgraveordfAgraveAring AiAgraveiAacuteordfAgraveAringzAgraveAElig Cregegrave


20 Physics

63 Which one of the following is true

(A) Bohr magneton is more than nuclear magneton

(B) Bohr magneton is equal to nuclear magneton

(C) Nuclear magneton is more than Bohr magneton

(D) Bohr and nuclear magnetons cannot be compared

F PEacutefrac14AgraveVpoundAgraveordfAgraveAringUAgravefrac14Agravedegegrave AiAgraveiAacuteordfAgraveAringzAgraveAuml cedilAgravej EzEacute

(A) poundAgraveAEligaringQegraveAiAgraveiAacutegiuml ordfAgraveiAacutearingUEacuteszligmAacutepoundiumlVAvAgrave umlEacuteAEligiacuteAtildegiuml ordfAgraveiAacutearingUEacuteszligmAacutepoundiuml ordmEacuteZAgraveAumlNtilde

(B) umlEacuteAEligiacuteAtildegiuml ordfAgraveiAacutearingUEacuteszligmAacutepoundiuml EzAgraveAuml poundAgraveAEligaringQegraveAiAgraveAumlgiuml ordfAgraveiAacutearingUEacuteszligmAacutepoundiumlUEacute cedilAgraveordfAgraveAuml

(C) umlEacuteAEligiacuteAtildegiuml ordfAgraveiAacutearingUEacuteszligmAacutepoundiumlVAvAgrave poundAgraveAEligaringQegraveAiAgraveAumlgiuml ordfAgraveiAacutearingUEacuteszligmAacutepoundiuml ordmEacuteZAgraveAumlNtilde

(D) umlEacuteAEligiacuteAtildegiuml ordmAacuteUAgraveAElig poundAgraveAEligaringQegraveAiAgraveAumlgiuml ordfAgraveiAacutearingUEacuteszligmAacutepoundiumlUAgravefrac14AgravepoundAgraveAumlszlig ordmEacuteAEligAtildedegcedilAgrave5AacuteUAgravezAgraveAuml

64 For a scintillation detector which one of the following statements is incorrect

(A) It detects nuclear radiation

(B) It operates at high voltages

(C) It does not give the energy of the particles detected

(D) It gives the number of particles emitted per second

sup1currenOuml5EacuteAtildemicroAgravepoundiuml acutetrade ethrsquoaringplusmnsup2microoacute˜microeth cedilAgraveAsectAcentuumlsup1zAgraveAvEacute F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgrave ordmEacuteAtildefrac12PEacuteAiAgraveAumlAuml cedilAgravejAiAgraveiAacuteVgAgraveAumlordfAgraveAringcentregegrave

(A) EzAgraveAuml poundAgraveAEligaringQegraveAiAgraveiAacutegiuml laquoQgAgravetordfAgravepoundAgraveAumlszlig yenAgravevEacuteUcirc ordfAgraveiAacuteqAgraveAumlvAgraveUcirczEacute

(B) EzAgraveAuml ordmEacuteEcircordfEacuteCcedilAtilde5EacuteOumlAtildeeiumlpoundAgravedegegrave PAacuteAiAgraveAumleth currenordfAgraveethraquocedilAgraveAumlvAgraveUcirczEacute

(C) EzAgraveAuml yenAgravevEacuteUcircAiAgraveiAacutezAgrave PAgravetUAgravefrac14Agrave plusmnAgraveQUcircAiAgraveAumlpoundAgraveAumlszlig currenAtildeqAgraveAumlordfAgraveAringcentregegrave

(D) EzAgraveAuml yenAgraveaeligw PAgraveeumltPEacuteIgrave GvAgraveigravefethvAgraveordfAacutezAgrave PAgravetUAgravefrac14Agrave cedilAgraveASEacutearingAiAgraveAumlpoundAgraveAumlszlig currenAtildeqAgraveAumlvAgraveUcirczEacute

65 Alpha particle is heavier than electron roughly by

(A) 7 times (B) 73 times

(C) 730 times (D) 7300 times

cedilAacuteordfAgraveiAacutepoundAgravearingordfAacuteV α PAgravetordfAgraveAring J5EacutePAacuteOumlccedilpoundiumlVAvAgrave F PEacutefrac14AgraveVpoundAgravemicroAgraveAumlOuml sAacutegAgraveordfAacuteVgAgraveAumlvAgraveUcirczEacute

(A) 7 yenAgravelAumlOuml (B) 73 yenAgravelAumlOuml

(C) 730 yenAgravelAumlOuml (D) 7300 yenAgravelAumlOuml


Physics 21

66 In case of K- electron capture which one of the following statement is correct

(A) The mass and atomic number remain same

(B) The mass number remain same atomic number increases by one

(C) The mass number changes but atomic number remains same

(D) The mass number remains same but neutron number increases

K- J5EacutePAacuteOumlccedilpoundiuml PAacutearingyenAgraveNtildegiumlUEacute cedilAgraveAsectAcentuumlsup1zAgraveAvEacute F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgrave ordmEacuteAtildefrac12PEacute cedilAgravejAiAgraveiAacuteVzEacute

(A) zAgraveaeligordfAgravearinggAacutesup2 ordmAacuteUAgraveAElig yenAgravegAgraveordfAgraveiAacutetAuml cedilAgraveASEacutearing sectzAgrave5AacuteUAgraveAumlordfAgraveAringcentregegrave

(B) zAgraveaeligordfAgravearinggAacutesup2 cedilAgraveASEacutearing ordmAacuteUEacuteAiEacuteAumlAtilde Gfrac12AiAgraveAumlAumlvAgraveUcirczEacute yenAgravegAgraveordfAgraveiAacutetAuml cedilAgraveASEacutearing MAzAgraveAQ ordmEacuteZAacuteNtildeUAgraveAumlvAgraveUcirczEacute

(C) zAgraveaeligordfAgravearinggAacutesup2 cedilAgraveASEacutearingAiAgraveAumlAuml sectzAgrave5AacuteUAgraveAumlvAgraveUcirczEacute DzAgravegEacute yenAgravegAgraveordfAgraveiAacutetAuml cedilAgraveASEacutearing ordmAacuteUEacuteAiEacuteAumlAtilde Gfrac12AiAgraveAumlAumlvAgraveUcirczEacute

(D) zAgraveaeligordfAgravearinggAacutesup2 cedilAgraveASEacutearingAiAgraveAumlAuml ordmAacuteUEacuteAiEacuteAumlAtilde Gfrac12AiAgraveAumlAumlvAgraveUcirczEacute DzAgravegEacute poundAgraveAEligaringmAacuteaeligpoundiuml cedilAgraveASEacutearing ordmEacuteZAacuteNtildeUAgraveAumlvAgraveUcirczEacute

67 In which of the following nuclear binding energy per nucleon is highest

F PEacutefrac14AgraveVpoundAgraveordfAgraveAringUAgravefrac14Agravedegegrave AiAgraveiAacuteordfAgraveAringzAgraveAuml yenAgraveaeligw poundAgraveAEligaringQegraveAiAgraveiAacutepoundiumlUEacute Cw ordmEacuteZAgraveAumlNtilde AumlaringeumlIumlldquoOacutesup2igravearingecircsup2microoacute sectAzsAgravePAgrave plusmnAgraveQUcircAiAgraveAumlpoundAgraveAumlszlig ordmEacuteAEligAcentgAgraveAumlvAgraveUcirczEacute

(A) U238 (B) Fe56

(C) Ag107 (D) Pb206

68 Rotational symmetry of a triclinic unit cell is

(A) Two fold (B) Three fold

(C) Four fold (D) Five fold

MAzAgraveAuml mEacuteaeligoumlEcircQegravecurrenPiuml PEacuteAEligAtildeplusmnAgrave WAgravelPAgravezAgrave DordfAgravevAgraveethcurrenAtildeAiAgraveAuml cedilAgravelaquoAumlaumlwAiAgraveAumlAuml

(A) JgAgraveqAgraveAuml ordfAgraveAumlrPEacute (B) ordfAgraveAumlAEliggAgraveAuml ordfAgraveAumlrPEacute

(C) poundAacuteregAumlIgrave ordfAgraveAumlrPEacute (D) ŒAacutemicroaringecirc Ocircaringecirc tradersquoeth

69 A lattice plane cuts x y and z-axis at 2a 3b and c respectively Which one of the following represents its Miller indices

MAzAgraveAuml 5Aacutearingncediliuml yenEacuteegraveAtildepoundiuml x y ordmAacuteUAgraveAElig z CPAgraveeumlUAgravefrac14AgravepoundAgraveAumlszlig CpoundAgraveAumlPAgraveaeligordfAgraveAumlordfAacuteV 2a 3b ordmAacuteUAgraveAElig c UAgravefrac14Agravedegegrave bEacuteAtildecentcedilAgraveAumlvAgraveUcirczEacute ordmAacuteUAacutezAgravegEacute EordfAgraveAringUAgravefrac14Agrave laquoAumlregegravegiuml EArsup1cediliuml KpoundAacuteVgAgraveAumlvAgraveUcirczEacute

(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics

70 The non-primitive cell of a lattice is usually chosen because it exhibits (A) Symmetry of lattice (B) Lattice parameter (C) Angles of unit cell (D) None of these 5AacutearingncediliumlpoundAgrave poundAacutepoundiuml-brvbaraeliglaquoAumlnAtildeordfiuml PEacuteAEligAtildeplusmnAgraveordfAgravepoundAgraveAumlszlig DAiEacuteAumlIgrave ordfAgraveiAacuterPEacuteAEligfrac14AgraveicircregAuml PAacutegAgravetordfEacuteAtildepoundEacuteAzAgravegEacute CzAgraveAuml F

PEacutefrac14AgraveVpoundAgravezAgravepoundAgraveAumlszlig vEacuteAEligAtildeyenAgraveethrcedilAgraveAumlvAgraveUcirczEacute (A) 5AacutearingncediliumlpoundAgrave cedilAgravelaquoAumlaumlw (B) 5AacutearingncediliumlpoundAgrave yenAgraveaeliglaquoAumlw (C) PEacuteAEligAtildeplusmnAgrave WAgravelPAgravezAgrave PEacuteAEligAtildepoundAgraveUAgravefrac14AgraveAuml (D) ordfEacuteAumlAtildedegpoundAgraveordfAgraveAring AiAgraveiAacuteordfAgraveAringzAgraveAElig Cregegrave

71 A free electron in a metal has the random velocity of 2 times 106 m-sndash1 Itrsquos de Broglie wavelength is

5EacuteAEligAtildeordmAgravezAgravedegegravegAgraveAumlordfAgrave MAzAgraveAuml ordfAgraveAumlAumlPAgraveUcirc J5EacutePAacuteOumlccedilpoundiumlpoundAgrave gAacutearingAqAgraveordfAgraveiiuml ordfEacuteAtildeUAgrave 2 times 106 m-sndash1 CpoundAgraveAumlszlig ordmEacuteAEligAcentzAacuteYacuteUAgrave CzAgravegAgrave r-umlEacuteAEligaeligAtildeVegraveAtilde vAgravegAgraveAUAacuteAvAgravegAgrave JmicroAgraveAumlOuml

(A) 36 Aring (B) 10 Aring

(C) 52 Aring (D) 49 Aring

72 If the electron concentration in a metal is 845 times 1028 mndash3 then its Fermi energy is given by

MAzAgraveAuml 5EacuteAEligAtildeordmAgravezAgravedegegrave J5EacutePAacuteOumlccedilpoundiuml cedilAacuteAzAgraveaeligvEacuteAiAgraveAumlAuml 845 times 1028 mndash3 DVzAgraveYacutegEacute CzAgravegAgrave yensAgravelaquoAumleth JpoundEacutefeth JmicroAgraveAumlOuml

(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV

73 The constant value of the Lorentz number in metals indicates that electrical and thermal currents are mainly carried by

(A) Phonons (B) Electrons

(C) Both phonons and electrons (D) Holes

5EacuteAEligAtildeordmAgravezAgravedegegravepoundAgrave 5EacuteAEliggAacutearingAmiumlOacute cedilAgraveASEacutearingAiAgraveAumlAuml sup1UumlgAgraveordfAacuteVzAacuteYacuteUAgrave F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgrave PAgravetUAgravefrac14AgraveAuml laquozAgraveAumlaringviuml ordfAgraveAumlvAgraveAumlUcirc GmicroAgraveUacute yenAgraveaeligordfAacuteordmAgraveUAgravefrac14AgravepoundAgraveAumlszlig ordmEacuteAEligvEacuteAEligUcircAiAgraveAumlAumlaringvAgraveUcircordfEacute JAsectAumlzAgravepoundAgraveAumlszlig cedilAgraveAEligacedilAgraveAumlvAgraveUcirczEacute

(A) yensEacuteAEligAtildepoundAacutepoundiumlUAgravefrac14AgraveAuml

(B) J5EacutePAacuteOumlccedilpoundiumlUAgravefrac14AgraveAuml

(C) yensEacuteAEligAtildepoundAacutepoundiuml ordfAgraveAumlvAgraveAumlUcirc J5EacutePAacuteOumlccedilpoundiumlUAgravefrac14EacutegAgraveqAgraveAElig

(D) szligetheumlNtildeoacuteTHORN microaringacircyumlaringecirc


Physics 23

74 A metal has Fermi energy of electron is 55 eV Then its Fermi velocity will be

MAzAgraveAuml 5EacuteAEligAtildeordmAgravezAgravedegegravepoundAgrave J5EacutePAacuteOumlccedilpoundiumlpoundAgrave yensAgravelaquoAumleth plusmnAgraveQUcircAiAgraveAumlAuml 55 eV DVzAgraveYacutegEacute CzAgravegAgrave yensAgravelaquoAumleth ordfEacuteAtildeUAgraveordfEacutemicroAgraveAumlOuml

(A) 25 times 106 ms (B) 14 times 106 ms

(C) 10 times 106 ms (D) 50 times 105 ms

75 In Kronig-Penney model if the barrier for Bloch electron becomes extremely strong then

the allowed energy levels of an electron become

(A) Discrete (B) Continuous

(C) Quasi continuous (D) None of these

PEacuteAEligaeligAtildecurrenUiuml-yenEacutecurrenszlig ordfAgraveiAacutezAgravejAiAgraveAumldegegrave umlAacuteegraveocircoacute J5EacutePAacuteOumlccedilpoundiumlpoundAgrave umlAacutearingjAiAgraveAumlgiuml yenAgraveaeligsectregordfAacuteVzAgraveYacutegEacute DUAgrave

J5EacutePAacuteOumlccedilpoundiumlpoundAgrave cedilAgraveordfAgraveAumlaumlwcedilAgraveAumlordfAgraveAvAgraveordmAgrave plusmnAgraveQUcirc ordfAgraveAumllOumlUAgravefrac14AgraveAuml KpoundAacuteUAgraveAumlvAgraveUcircordfEacute

(A) CcedilEgravearingETHfrac14ethIumleacutersquoaringordfAacuteUAgraveAumlvAgraveUcircordfEacute

(B) currengAgraveAvAgravegAgraveordfAacuteUAgraveAumlvAgraveUcircordfEacute

(C) sAacuteUAgraveplusmnAgraveB currengAgraveAvAgravegAgraveordfAacuteUAgraveAumlvAgraveUcircordfEacute

(D) ordfEacuteAumlAtildedegpoundAgraveordfAgraveAring AiAgraveiAacuteordfAgraveAringzAgraveAElig Cregegrave

76 The force experienced by an electron due to an external electric field in a periodic

potential is given by

DordfAgravevAgraveethpoundAgrave laquo sAgraveordfAgravezAgravedegegravepoundAgrave umlAacuteordmAgravearing laquozAgraveAumlaringviuml PEacuteeumlAtildevAgraveaeligzAgrave yenAgraveaelig sAacuteordfAgravecentAzAacuteV J5EacutePAacuteOumlccedilpoundiumlpoundAgrave ordfEacuteAumlAtilde5Eacute

GAmAacuteUAgraveAumlordfAgrave sectregordfAgravepoundAgraveAumlszlig F PEacutefrac14AgraveVpoundAgrave cedilAgravelaquoAumlAtildePAgravegAgravetcentAzAgrave PAgraveAqAgraveAumlraquorAiAgraveAumlsectordmAgraveAumlzAgraveAuml

(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

77 The dispersion curves of electrons 1 and 2 are shown in the following figure

The effective mass of

(A) Electron 1 is more than electron 2

(B) Electron 2 is more than electron 1

(C) Electron 2 is less than electron 1

(D) Electron 1 and 2 are same

J5EacutePAacuteOumlccedilpoundiuml 1 ordfAgraveAumlvAgraveAumlUcirc 2 gAgrave yenAgraveaeligcedilAgravegAgravet cedilAgraveAsectAzsAgraveUAgravefrac14AgravepoundAgraveAumlszlig F PEacutefrac14AgraveVpoundAgrave avAgraveaeligzAgravedegegrave currenAtildeqAgrave5AacuteVzEacute DUAgrave yenAgravejuAacuteordfAgraveiAacutePAacutej zAgraveaeligordfAgravearinggAacutesup2

(A) J5EacutePAacuteOumlccedilpoundiuml 1 gAgravezAgraveAuml J5EacutePAacuteOumlccedilpoundiuml 2 QIgraveAvAgrave ordmEacuteaNtildegAgraveAumlvAgraveUcirczEacute (B) J5EacutePAacuteOumlccedilpoundiuml 2 gAgravezAgraveAuml J5EacutePAacuteOumlccedilpoundiuml 1 QIgraveAvAgrave ordmEacuteaNtildegAgraveAumlvAgraveUcirczEacute (C) J5EacutePAacuteOumlccedilpoundiuml 2 gAgravezAgraveAuml J5EacutePAacuteOumlccedilpoundiuml 1 QIgraveAvAgrave PAgraverordfEacuteAumlnotAumlgAgraveAumlvAgraveUcirczEacute (D) J5EacutePAacuteOumlccedilpoundiuml 1 ordfAgraveAumlvAgraveAumlUcirc J5EacutePAacuteOumlccedilpoundiuml 2 gAgravezAgraveAuml cedilAgraveordfAgraveAumlordfAacuteVgAgraveAumlvAgraveUcirczEacute

78 The mobility micro of an electron in a semiconductor at high temperature is given by

CcentuumlPAgrave GmicroAgraveUacutevEacuteAiAgraveAumldegegravegAgraveAumlordfAgrave CgEacuteordfAacuteordmAgravePAgravezAgravedegegravepoundAgrave J5EacutePAacuteOumlccedilcurrenpoundAgrave ZAgraveregpoundAgravesup2AtilderegvEacute (micro) F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgraveAringzAgravegAgraveAvEacute EgAgraveAumlvAgraveUcirczEacute

(A) micro α T (B) micro α Tndash1

(C) micro α Tndash32 (D) micro α Tndash2

79 Average radius of an electron in a closed shell atom is ltrgtThe diamagnetic susceptibility as per Langevin theory is proportional to

cedilAgraveAordfAgraveEgravevAgrave plusmnEacute5iuml CtAumllaquopoundAgrave CAzAacutefvAgrave J5EacutePAacuteOumlccedilpoundiuml waeligdaringordfAgraveAring ltrgt DVzAacuteYacuteUAgrave 5AacutearingAeEacutelaquopoundiuml sup1zAacuteTHORNAvAgravezAgraveAvEacute CpoundAgraveAumlPAacuteAwAtildeAiAgraveAumlvEacuteAiAgraveAuml UAacuteaeligordmAgravePAgravevAgraveeacuteordfAgraveAring F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgraveAringzAgravePEacuteIgrave CpoundAgraveAumlyenAacutevAgraveordfAacuteVgAgraveAumlvAgraveUcirczEacute

(A) ltrgt (B) ltr3gt

(C) ltr2gt (D) ltr4gt

k

E 1

2

k

E 1

2


Physics 25

80 A superconductor has Tc = 72 K and Hc(0) = 803 Gauss What is the critical magnetic

field required to destroy its superconducting state at 5 K

MAzAgraveAuml CcentuumlordfAacuteordmAgravePAgraveordfAgraveAring Tc = 72 K ordfAgraveAumlvAgraveAumlUcirc Hc(0) = 803 Gauss ordmEacuteAEligAcentzAacuteYacuteUAgrave 5 K GmicroAgraveUacutevEacuteAiAgraveAumldegegrave CzAgravegAgrave CcentuumlordfAacuteordmAgravePAgravevEacuteAiAgraveAumlpoundAgraveAumlszlig poundAacuteplusmnAgraveyenAgraversup1regAuml CUAgravevAgravearingordfAacuteV umlEacuteAtildePAacuteUAgraveAumlordfAgrave PAacuteaeligAw CAiAgraveAumlcedilAacuteIgraveAwAtildeAiAgraveAuml PEacuteeumlAtildevAgraveaeligordfEacutemicroAgraveAumlOuml

(A) 800 Gauss (B) 750 Gauss

(C) 671 Gauss (D) 416 Gauss

81 In ac Josephson effect an applied ac voltage of 1 microV produces a frequency of

1 microV poundAgravemicroAgraveAumlOuml ac ordfEacuteCcedilAtilde5EacuteOumlAtildeeiuml CpoundAgraveeacutenotAumlvAgrave DzAacuteUAgrave Jsup1 eEacuteAEligAtildecedilEacuteyensAgraveigravepoundiuml yenAgravejuAacuteordfAgraveAumlzAgravedegegrave JmicroAgraveAumlOuml DordfAgravevAacuteethAPAgrave GAmAacuteUAgraveAumlvAgraveUcirczEacute

(A) 4505 MHz (B) 4752 MHz

(C) 4836 MHz (D) None of these

82 The direction of molecular alignment progressively twists with depth in

(A) Nematic phase (B) Cholesteric phase

(C) Smectic phase (D) Nano phase CtAcirceacutePAgrave eEacuteAEligAtildeqAgraveuEacute centplusmnEacute ordmEacuteZAacuteNtildeUAgraveAumlwUcircgAgraveAumlordfAgrave Dfrac14AgravezEacuteAEligAcentUEacute F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgrave yensEacuteAtildecediliumlpoundAgravedegegrave

sectzAgrave5AacuteUAgraveAumlvAgraveUcirczEacute (A) poundEacuteordfAgraveiAacutearingnPiuml yensEacuteAtildecediliuml (B) PEacuteAElig5EacutecedilEacuteOumljPiuml yensEacuteAtildecediliuml (C) cedilEacuteaumlQOumlPiuml yensEacuteAtildecediliuml (D) poundAacutearingpoundEacuteAEligAtilde yensEacuteAtildecediliuml

83 The reason we call an astronomical body as black hole because

(A) it is a huge star which appears black at its centre

(B) its gravity is so high that it absorbs its own photons

(C) it represents lack of matter in a portion of space

(D) it is a dead planet MAzAgraveAuml RUEacuteAEligAtildefrac14Agrave PAacuteAiAgraveAumlordfAgravepoundAgraveAumlszlig PAgraveyenAgraveAumlagrave gAgraveAzsAgraveaeligordfEacuteAzAgraveAuml PAgravegEacuteAiAgraveAumlregAuml EgAgraveAumlordfAgrave PAacutegAgravet (A) CzAgraveAuml vAgravepoundAgraveszlig PEacuteAtildeAzAgraveaeligzAgravedegegrave PAgraveyenAacuteagraveV PAgraveAqAgraveAumlsectgAgraveAumlordfAgrave zEacuteEcircvAgravearing poundAgravePAgraveeumlvAgraveaelig (B) CzAgravegAgrave UAgraveAumlgAgraveAumlvAgraveeacute JmicroAgraveAumlOuml ordmEacuteaNtildegAgraveAumlvAgraveUcirczEacuteAzAgravegEacute CzAgraveAuml vAgravepoundAgraveszligzEacuteAtilde yensEacuteAEligAtildemAacutepoundiumlUAgravefrac14AgravepoundAgraveAumlszlig

raquoAtildejPEacuteAEligfrac14AgraveAumlicircvAgraveUcirczEacute (C) CAvAgravejPAgraveeumlzAgrave sAacuteUAgraveordfEacuteCcedilAzAgravegAgravedegegrave zAgraveaeligordfAgravearingzAgrave PEacuteAEliggAgravevEacuteAiAgraveAumlpoundAgraveAumlszlig cedilAgraveAEligacedilAgraveAumlvAgraveUcirczEacute (D) CzEacuteAEligAzAgraveAuml ordfAgraveAumlEgravevAgrave UAgraveaeligordmAgraveordfAacuteVgAgraveAumlvAgraveUcirczEacute


26 Physics

84 The H-R diagram of stars directly compares the following properties of stars (A) Size and density (B) Temperature and luminosity (C) Density and luminosity (D) Distance and temperature poundAgravePAgraveeumlvAgraveaeligUAgravefrac14Agrave H-R gEacuteAtildeSAacuteavAgraveaeligordfAgraveAring AumlaringrsquoaringUcircfrac14aringETH microaringacircyumlaring F PEacutefrac14AgravePAgraveAqAgrave UAgraveAumltregPAgraveeumltUAgravefrac14AgravepoundAgraveAumlszlig poundEacuteAtildegAgraveordfAacuteV ordmEacuteAEligAtildedegcedilAgraveAumlvAgraveUcirczEacute (A) UAacutevAgraveaelig ordfAgraveAumlvAgraveAumlUcirc cedilAacuteAzAgraveaeligvEacute (B) GmicroAgraveUacutevEacute ordfAgraveAumlvAgraveAumlUcirc centAtildeyenAgraveUcircvEacute (C) cedilAacuteAzAgraveaeligvEacute ordfAgraveAumlvAgraveAumlUcirc centAtildeyenAgraveUcircvEacute (D) CAvAgravegAgrave ordfAgraveAumlvAgraveAumlUcirc GmicroAgraveUacutevEacute

85 A pulsar is actually a (A) black hole (B) white dwarf (C) red giant (D) neutron star cedilAacuteordfAgraveiAacutepoundAgravearingordfAacuteV yenAgraveregigravegiuml JAzAgravegEacute (A) PAgraveyenAgraveAumlagrave gAgraveAzsAgraveaelig (B) plusmnEacuteeacuteAtildevAgrave PAgraveAumlsectOacute (C) PEacuteAyenAgraveAuml zEacuteEcircvAgravearing (D) poundAgraveAEligaringmAacuteaeligpoundiuml poundAgravePAgraveeumlvAgraveaelig

86 A star like object with a very large red shift is a (A) Quasar (B) Neutron star (C) Nova (D) Supernova Cw ordmEacuteZAgraveAumlNtilde PEacuteAyenAgraveAuml yenAgraveregegravel ordmEacuteAEligAcentgAgraveAumlordfAgrave poundAgravePAgraveeumlvAgraveaeligordfAgraveAring F PEacutefrac14AgraveVpoundAgravezAacuteYacuteVgAgraveAumlvAgraveUcirczEacute (A) PAacuteeacutecedilAgravegiuml (B) poundAgraveAEligaringmAacuteaeligpoundiuml poundAgravePAgraveeumlvAgraveaelig (C) poundEacuteAEligAtildeordfAacute (D) cedilAgraveAEligyenAgravegiuml poundEacuteAEligAtildeordfAacute

87 A first magnitude star is brighter than a second magnitude star by ordfEacuteAEligzAgravereg yenAgravejordfAgraveiAacutet poundAgravePAgraveeumlvAgraveaeligordfAgraveAring JgAgraveqAgravepoundEacuteAtilde yenAgravejordfAgraveiAacutet poundAgravePAgraveeumlvAgraveaeligQIgraveAvAgrave JmicroAgraveAumlOuml yenAgravelAumlOuml GdeacuteregordfAacuteVgAgraveAumlvAgraveUcirczEacute (A) 25 times (B) 73 times (C) 2 times (D) 10 times

88 If there are n generalized coordinates in a system the number of Hamiltonrsquos equations are MAzAgraveAuml ordfAgravearingordfAgravecedilEacuteUumlAiAgraveAumldegegrave n cedilAacuteordfAgraveethwaeligAtildePAgravejsup1zAgrave currenzEacuteethAtildeplusmnAacuteAPAgraveUAgravefrac12zAgraveYacutegEacute ordmAacutearinglaquoAumlregOumlpoundiumlpoundAgrave cedilAgravelaquoAumlAtildePAgravegAgravetUAgravefrac14Agrave

cedilAgraveASEacutearingAiAgraveAumlAuml (A) n (B) 2n (C) 3n (D) n2

89 Under Galilean transformation the acceleration is as measured by the observers in two frames of references

(A) remains invariant (B) are different (C) is zero (D) None of the above UEacutedegdegAiEacuteAumlpoundiuml yenAgravejordfAgravevAgraveethpoundEacuteAiAgraveAuml yenAgraveaeligPAacutegAgrave ordfEacuteAtildeUEacuteAEligAtildevAgraveIgravemicroAgraveethordfAgraveAring Aringsup2tradeeacutersquoaringUcircrsquoaringsup2microaringecirc Šsup2microaring microaringecirc ocircograversquoaringdegplusmnAumlaringNtildendashOacute DaggerNtildeethOacuteeacutebullndashUumlYacute

OcircaringigraveaeligCcedilYacuteUumlYacuteAacutemicroaringOgravefrac14eth (A) sup2tradeOcircethecircntildeAumloacuteTHORN hellipAumlethOumleacutesup2tradesup2igravearingecircOgravemacroacute (B) EcircndashmiddotAumlaringAEligOcircaelig˜tradesup2microaringecircfrac14aringfrac34Aacutemicroeth (C) timesaringeumlAumlaringIumlOcircaelig˜tradesup2microaringecircfrac14aringfrac34Aacutemicroeth (D) OcircethecirceacuteNtildendashAumlaring sup2igravearingigraveaeligOcircaringiacuteuacuteAacutemicroaringeuml ƒNtildeOacute


Physics 27

90 The angular speed of the earthrsquos rotation in itrsquos orbit around the sun per hour is cedilAgraveAEligAiAgraveAumlethpoundAgrave cedilAgraveAumlvAgraveUcirc vAgravepoundAgraveszlig PAgravePAacuteeumlAPAgravezAgravedegegrave yenAgravej sAgraveaeliglaquoAumlcedilAgraveAumlordfAgrave sAgraveAEliglaquoAumlAiAgraveAuml PEacuteAEligcurrenAtildeAiAgraveiAacute ordfEacuteAtildeUAgraveordfAgraveAring yenAgraveaeligw UAgraveAmEacuteUEacute

(A) π

24 (B)

π

12

(C) π

6 (D)

π

60

91 The theoretical limiting values of Poissionrsquos ratio (σ) are (A) 0 and 1 (B) ndash1 and 05 (C) 02 and 04 (D) ndash1 and 1 yenAacutenotAumlcedilAacutepoundiuml currenmicroAgraveagravewUcirc (σ) AiAgraveAuml cedilEacuteEcirczAacuteTHORNAwPAgrave yenAgravejlaquoAumlwAtildeAiAgraveAuml ordfAgraveiEumlregaringUAgravefrac14AgraveAuml (A) 0 ordfAgraveAumlvAgraveAumlUcirc 1 (B) ndash1 ordfAgraveAumlvAgraveAumlUcirc 05

(C) 02 ordfAgraveAumlvAgraveAumlUcirc 04 (D) ndash1 ordfAgraveAumlvAgraveAumlUcirc +1

92 A simple pendulum has a hollow bob filled with a liquid As the pendulum oscillates the liquid leaks out of a hole in the bob The period of oscillation of the pendulum will then

(A) remain constant throughout (B) decrease as a function of time (C) increase as a function of time (D) increase in the beginning and then decrease back to the original value MAzAgraveAuml cedilAgravegAgravefrac14Agrave 5EacuteAEligAtilderegPAgraveordfAgraveAring zAgraveaeligordfAgrave vAgraveAumlAcopyzAgrave mEacuteAEligfrac14AgraveAumlicirc vAgraveAEligUAgraveAumlUAgraveAumlAqAgravepoundAgraveAumlszlig ordmEacuteAEligAcentzEacute 5EacuteAEligAtilderegPAgraveordfAgraveAring

DAzEacuteAEligAtilderegpoundAgraveUEacuteAEligAqAgraveAvEacute vAgraveAEligUAgraveAumlUAgraveAumlArpoundAgrave gAgraveAzsAgraveaeligcentAzAgrave zAgraveaeligordfAgraveordfAgraveAring cedilEacuteAEligAtildejPEacuteAiAgraveiAacuteUAgraveAumlvAgraveUcirczEacute ordmAacuteUAacutezAgravegEacute 5EacuteAEligAtilderegPAgravezAgrave DAzEacuteAEligAtilderegpoundAgravezAgrave cedilAgraveordfAgraveAumlAiAgraveAumlordfAgraveAring

(A) sup1UumlgAgraveordfAacuteV Gfrac12AiAgraveAumlAumlvAgraveUcirczEacute (B) cedilAgraveordfAgraveAumlAiAgraveAuml PAgravefrac14EacutezAgraveAvEacute PAgraverordfEacuteAumlAiAgraveiAacuteUAgraveAumlvAgraveUcirczEacute (C) cedilAgraveordfAgraveAumlAiAgraveAuml PAgravefrac14EacutezAgraveAvEacute ordmEacuteZAacuteNtildeUAgraveAumlvAgraveUcirczEacute (D) yenAacuteaeliggAgraveA sAgravezAgravedegegrave ordmEacuteZAacuteNtildeUAgraveAumlvAgraveUcirczEacute ordfAgraveAumlvAgraveAumlUcirc cedilAgraveordfAgraveAumlAiAgraveAuml PAgravefrac14EacutezAgraveAvEacute PAgraverordfEacuteAumlAiAgraveiAacuteUAgraveAumlvAacuteUcirc ordfAgraveAumlAEligreg

ordfAgraveiEumlregaringzAgravemicroAacuteOumlUAgraveAumlvAgraveUcirczEacute

93 Canonical transformations (A) leave the Poisson brackets invariant (B) change the Lagrangian to the Hamiltonian (C) are only useful if the Hamiltonian is symmetric (D) can be used to convert the Hamiltonian PEacutepoundEacuteAEligAtildecurrenPAgrave5iuml yenAgravejordfAgravevAgraveethpoundEacuteUAgravefrac12UEacute cedilAgraveAsectAcentuumlsup1zAgraveAvEacute F PEacutefrac14AgraveVpoundAgraveordfAgraveAringUAgravefrac14Agravedegegrave AiAgraveiAacuteordfAgraveAringzAgraveAuml cedilAgravejAiAgraveiAacuteVzEacute (A) CordfAgraveAring yenAacutenotAumlcedilAgravepoundiuml umlAacuteaeligPEacutemiumlUAgravefrac14AgravepoundAgraveAumlszlig hellipAumlethOumleacutesup2tradesup2igravearingecircOgravemacroacute˜microeth ƒAumlaringecircOcircaringecircfrac12UumlEgravearingecircfrac14aringfrac34Aacutemicroeth (B) CordfAgraveAring 5EacuteUAacuteaeligAfAiEacuteAumlpoundiuml CpoundAgraveAumlszlig ordmAacutearinglaquoAuml5EacuteAEligOumlcurrenAiEacuteAumlpoundiuml DV sectzAgrave5AacutenotAumlcedilAgraveAumlvAgraveUcirczEacute (C) CordfAgraveAring ordmAacutearinglaquoAuml5EacuteAEligOumlcurrenAiEacuteAumlpoundiuml cedilAgravelaquoAumlaumlw EzAacuteYacuteUAgrave ordfAgraveiAacutevAgraveaelig GyenAgraveAiEacuteAEligAtildeUAgraveordfAacuteUAgraveAumlvAgraveUcircordfEacute (D) CordfAgraveAring ordmAacutearinglaquoAuml5EacuteAEligOumlcurrenAiEacuteAumlpoundiuml CpoundAgraveAumlszlig yenAgravejordfAgravewethcedilAgraveregAuml sectfrac14AgravecedilAgravesectordmAgraveAumlzAgraveAuml


28 Physics

94 The normal modes in small oscillations are (A) perpendicular to the actual motion (B) the same as the eigenvectors (C) the frequencies in an oscillating pendulum (D) dependent on the coordinates chosen cedilAgravetUacute DAzEacuteAEligAtilderegpoundAgraveUAgravefrac14Agravedegegrave cedilAacuteordfAgraveiAacutepoundAgravearing ordfEacuteAEligqiumlUAgravefrac14AgraveAuml (A) ordfAacutecedilAgraveUcirclaquoPAgrave ZAgraveregpoundEacuteUEacute regAsectordfAacuteVgAgraveAumlvAgraveUcircordfEacute (B) LUAgravepoundiuml cedilAgravecentplusmnAgravezAgraveAvEacuteAiEacuteAumlAtilde EgAgraveAumlvAgraveUcircordfEacute (C) DAzEacuteAEligAtilderegpoundAgraveUEacuteAEligfrac14AgraveAumlicircwUcircgAgraveAumlordfAgrave 5EacuteAEligAtilderegPAgravezAgravedegegravepoundAgrave DordfAgravevAacuteethAPAgraveUAgravefrac14AacuteVgAgraveAumlvAgraveUcircordfEacute (D) DAiEacuteAumlIgrave ordfAgraveiAacutergAgraveAumlordfAgrave currenzEacuteethAtildeplusmnAacuteAPAgraveUAgravefrac14Agrave ordfEacuteAumlAtilde5Eacute CordfAgraveregAcopysup1ordfEacute

95 Complimentary function of a differential equation xydx

dyx

dx

ydx log2

2

22

=+minus is

where Zex =

CordfAgravePAgraveregpoundAgrave cedilAgravelaquoAumlAtildePAgravegAgravet xydx

dyx

dx

ydx log2

2

22

=+minus EzAgravegAgrave yenAgraveAEliggAgravePAgrave yensAgraveregpoundAgraveordfAgraveAring F PEacutefrac14AgraveVpoundAgrave

AiAgraveiAacuteordfAgraveAringzAgraveAuml DVgAgraveAumlvAgraveUcirczEacute Edegegrave Zex =

(A) ZeZCC )( 21 + (B) ZeZCC )( 21 minus

(C) ZeZCC minus+ )( 21 (D) ZeZCC minus

minus )( 21

96 The equation 0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is

(A) Legendrersquos differential equation (B) Bessel differential equation (C) Laguerre differential equation (D) Hermite differential equation

0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd cedilAgravelaquoAumlAtildePAgravegAgravetordfAgraveAring

(A) 5EacuteeEacuteAqEacuteaelig poundAgrave CordfAgravePAgraveregpoundAgrave cedilAgravelaquoAumlAtildePAgravegAgravetordfAacuteVzEacute (B) umlEacutecedilEacuteigrave5iumlpoundAgrave CordfAgravePAgraveregpoundAgrave cedilAgravelaquoAumlAtildePAgravegAgravetordfAacuteVzEacute (C) 5AacutearingUAgravegEacuteaelig poundAgrave CordfAgravePAgraveregpoundAgrave cedilAgravelaquoAumlAtildePAgravegAgravetordfAacuteVzEacute (D) ordmAgravegEacuteaumloumlEcircmiuml poundAgrave CordfAgravePAgraveregpoundAgrave cedilAgravelaquoAumlAtildePAgravegAgravetordfAacuteVzEacute


Physics 29

97 Using Fourier series method the determined value of suminfin

=12

1

n n is

yensEacuteAEligAtildejAiAgraveAumlgiuml plusmnEacuteaeligAtildetAcirc laquozsAacutepoundAgraveordfAgravepoundAgraveAumlszlig sectfrac14Agravesup1PEacuteAEligAqAgraveAuml suminfin

=12

1

n n poundAgrave ordfAgraveiEumlregaringordfAgravepoundAgraveAumlszlig F PEacutefrac14AgraveVpoundAgrave

AiAgraveiAacuteordfAgraveAringzAgravegAgraveAvEacute currenzsAgraveethjcedilAgravesectordmAgraveAumlzAgraveAuml

(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π

98 Which one of the following axiom should be additionally satisfied by the Abelian group

when compared to normal group (A) Closure (B) Associativity (C) Existence of inverse (D) Commutativity cedilAacuteordfAgraveiAacutepoundAgravearing UAgraveAumlAbrvbarUEacute ordmEacuteAEligAtildedegsup1zAgravegEacute CcopyAtildedegAiAgraveAumlpoundiuml UAgraveAumlAyenAgraveAuml F PEacutefrac14AgraveVpoundAgrave AiAgraveiAacuteordfAgrave DQigraveAiEacuteAumlA CpoundAgraveAumlszlig

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99 As per Newton-Raphson method the value of 12 determined to four decimal places is

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(A) 34644 (B) 34641 (C) 34650 (D) 34645 100 Finite difference of second order can be expressed as JgAgraveqAgravepoundEacuteAiAgraveAuml PAgraveaeligordfAgraveAumlzAgrave yenAgravejlaquoAumlvAgrave ordfAgravearingvAacutearingcedilAgraveordfAgravepoundAgraveAumlszlig F PEacutefrac14AgravePAgraveAqAgraveAvEacute CcopyuumlordfAgravearingPAgraveUcircUEacuteAEligfrac12cedilAgravesectordmAgraveAumlzAgraveAuml

(A) )]()(2)2([)(2afhafhafaf ++minus+=nabla

(B) )]()(2)([)(2afhafhafaf +minusminus+=nabla

(C) )]()2(2)2([)(2afhafhafaf ++minusminus=nabla

(D) )]()2(2)3([)(2afhafhafaf ++minus+=nabla

____________


30 Physics



Physics 31


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cedilAgraveeacuteAiAgraveAumlA ordfAgraveiEumlregaringordfAgraveiAacuteyenAgravepoundAgravePAacuteIgraveV ordfAgraveAumlpoundEacuteUEacute PEacuteAEligAqEacuteAEligAiAgraveAumlaringregAuml PEacuteAEligqAgraveAumlvAacuteUcircgEacute 9 GvAgraveUcircgAgrave yenAgravewaeligPEacuteAiAgraveAuml poundAgravePAgraveregpoundAgraveAumlszlig MAzAgraveAuml ordfAgravemicroAgraveeth PAacutereg cedilAgraveAumlgAgraveQeumlvAgraveordfAacuteV Er 10 PAgravepoundAgraveszligqAgrave DordfAgraveEgravewUcircAiAgraveAuml yenAgraveaeligplusmnEacuteszligUAgravefrac14Agravedegegrave GvAgraveUcircjcedilAgraveAumlordfAgrave CumlsAgravearingyethUAgravefrac12UEacute PAgravepoundAgraveszligqAgravezAgravedegegrave ordfAgraveAumlAumlcentaeligvAgraveordfAacuteVgAgraveAumlordfAgrave yenAgraveaeligplusmnEacuteszligUAgravefrac14Agrave sectUEacuteIcirc KpoundAacutezAgravegAgraveAElig cedilAgraveAzEacuteAtildeordmAgravelaquozAgraveYacutedegegrave

EAVegraveAtildemicroiuml DordfAgraveEgravewUcircAiAgraveAuml yenAgraveaeligplusmnEacuteszligyenAgravewaeligPEacuteAiAgraveAumlpoundAgraveAumlszlig poundEacuteAEligAtildeqAgravesectordmAgraveAumlzAgraveAuml

GFGC


2 Physics

1 If A and B are the two non-parallel vectors and have equal magnitude then the angle between the vectors (A + B) and (A ndash B) must be

(A) 180deg (B) 90deg (C) Less than 90deg (D) Greater than 90deg A ordfAgraveAumlvAgraveAumlUcirc B UAgravefrac14AgraveAuml JgAgraveqAgraveAuml cedilAgraveordfAgraveAumlpoundAacuteAvAgravegAgraveordfAgraveregegravezAgrave cedilAgravecentplusmnAgraveUAgravefrac14AacuteVzAgraveAumlYacute cedilAgraveordfAgraveiAacutepoundAgrave yenAgraveaeligordfAgraveiAacutetordfAgravepoundAgraveAumlszlig

ordmEacuteAEligAcentzAgraveYacutegEacute DUAgrave (A + B) ordfAgraveAumlvAgraveAumlUcirc (A ndash B) cedilAgravecentplusmnAgraveUAgravefrac14Agrave poundAgraveqAgraveAumllaquopoundAgrave PEacuteAEligAtildepoundAgrave (A) 180deg (B) 90deg (C) 90deg VAvAgrave PAgraverordfEacuteAuml (D) 90deg VAvAgrave ordmEacuteZAgraveAumlNtilde 2 Newtonrsquos law of force can be stated as

(A) dt

dpF = (B)

dt

dF

x=

(C) dt

dvF = (D)

dt

daF =

Here p is the momentum x the displacement v the velocity and a the acceleration poundAgraveAEligaringlpoundiumlpoundAgrave sectregzAgrave currenAiAgraveAumlordfAgraveAumlordfAgravepoundAgraveAumlszlig raquoAtildeUEacuteAzAgraveAuml ordmEacuteAtildefrac14AgravesectordmAgraveAumlzAgraveAuml

(A) dt

dpF = (B)

dt

dF

x=

(C) dt

dvF = (D)

dt

daF =

Edegegrave p AiAgraveAumlAuml cedilAgraveAordfEacuteAtildeUAgrave x MAzAgraveAuml cedilAacuteUumlpoundAgraveyenAgraveregegravel v AiAgraveAumlAuml ordfEacuteAtildeUAgraveordfAacuteVzAgraveAumlYacute ordfAgraveAumlvAgraveAumlUcirc a ordfEacuteAtildeUEacuteAEligAtildevAgraveIgravemicroAgraveethordfAacuteVzEacute

3 The Coriolis force on a moving particle will be (A) Perpendicular to ω and v (B) Parallel to ω and v (C) Parallel to ω and Perpendicular to v (D) Perpendicular to ω and Parallel to v Here ω and v are the angular and linear velocities respectively MAzAgraveAuml ZAgravedegcedilAgraveAumlordfAgrave PAgravetzAgrave ordfEacuteAumlAtilde5Eacute PEacuteAEligjAiAgraveiAacutedegcediliuml sectregordfAgraveAring F PEacutefrac14AgraveVpoundAgraveAwgAgraveAumlvAgraveUcirczEacute (A) ω ordfAgraveAumlvAgraveAumlUcirc v UAgravefrac12UEacute regAsect (B) ω ordfAgraveAumlvAgraveAumlUcirc v UEacute cedilAgraveordfAgraveAumlpoundAacuteAvAgravegAgrave (C) ω UEacute cedilAgraveordfAgraveAumlpoundAacuteAvAgravegAgrave ordfAgraveAumlvAgraveAumlUcirc v UEacute regAsect (D) ω UEacute regAsect ordfAgraveAumlvAgraveAumlUcirc v cedilAgraveordfAgraveAumlpoundAacuteAvAgravegAgrave Edegegrave ω ordfAgraveAumlvAgraveAumlUcirc v PAgraveaeligordfAgraveAumlordfAacuteV PEacuteAEligcurrenAtildeAiAgraveAuml ordmAacuteUAgraveAElig gEacuteAtildeTAtildeAiAgraveAuml ordfEacuteAtildeUAgraveUAgravefrac14AacuteVgAgraveAumlvAgraveUcircordfEacute


Physics 3







(A)

minus+

minus

minus

121

2 11ln

VVa

bV

bVRT

(B)

minus+

minus

minus

212

1 11ln

VVa

bV

bVRT

(C)

minus

minus

+

minus

bV

bVa

VVRT

1

2

12

11ln

(D)

minus

minus

+

minus

bV

bVa

VVRT

2

1

21

11ln


4 Physics










Physics 5





6 Physics











(A)

+

=

)exp( i

ii

E

gn

βα

(B)

minus+

=

1)exp( i

ii

E

gn

βα

(C)

++

=

1)exp( i

ii

E

gn

βα

(D)

+minus

=

)exp(1 i

ii

E

gn

βα












Physics 7






(D) be zero









(A) [ ]1)exp(

8 3

minus

=

minus

Tkhc

hcE

Bλ

λπ (B)

[ ]1)exp(

8 5

+

=

minus

Tkhc

hcE

Bλ

λπ

(C) [ ]1)exp(

8 3

+

=

minus

Tkhc

hcE

Bλ

λπ (D)

[ ]1)exp(

8 5

minus

=

minus

Tkhc

hcE

Bλ

λπ


acceleration is



(C) 50 ms2 (D) 002 ms2


8 Physics






(A) 5593 Hz (B) 5593 Hz (C) 5593 Hz (D) 5593 Hz








Physics 9













10 Physics



(A) ρ

ε0 (B)

ρ

3ε0

(C) 4πr3

3 ρ

ε0 (D)

rρ

3ε0


(A) nabla rarr


rarr

E = 0

(C) nabla times

rarr

E = ndash part

rarr

B

partt (D) nabla

rarr

E = ρ




2 V = ndash 4πρ


2 V = ndash

ρ

ε0


(A) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J + micro0 ε0 part

rarr

E

partt

(B) nabla rarr

E = 0 nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt

(C) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J

(D) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt


Physics 11



(A) 0Bmicro

1B

micro

1and 0EE0BBσDD ||

22

||1

1

||2


perpperpperpperp

(B) 0B

micro

1B

micro

1and

t

BEE0BB0DD ||

22

||1

1

||2

||12121 =minus

part


perpperpperpperp

(C) 0B

micro

1B

micro


22

||1

1

||2


perpperpperpperp

(D) 0B

micro

1B

micro

1and 0EE0BB0DD ||

22

||1

1

||2


perpperpperpperp




(C) If L 0dlB =


(D) None of these








12 Physics








35 If rarr

n


k


rarr



rarr

n = rarr

k (B) rarr

n = ndash rarr

k

(C) rarr

n rarr

k = 0 (D) rarr

n times rarr

k = 0



Physics 13



(A) Bmicro

1 Eε

00

rr+ (B) B E

micro

ε

0

0rr

sdot

(C) 22

0

0 B E 2micro

εsdot (D)

+

2

0

20 B

micro

1Eε

2

1




















14 Physics











(A) (63 times 10)64 V (B) 1064 V

(C) 10 V (D) 64 V



(A) 3 (B) 1

(C) 0 (D) frac12











Physics 15









16 Physics







(A) 1 (B) 050 (C) 025 (D) 0









Physics 17






L

)sin(2πA)(ψ




)sin(2πA)(ψ








18 Physics




(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20


x+rarr NC14

7

14



x+rarr NC14

7

14














Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


Physics 3







(A)

minus+

minus

minus

121

2 11ln

VVa

bV

bVRT

(B)

minus+

minus

minus

212

1 11ln

VVa

bV

bVRT

(C)

minus

minus

+

minus

bV

bVa

VVRT

1

2

12

11ln

(D)

minus

minus

+

minus

bV

bVa

VVRT

2

1

21

11ln


4 Physics










Physics 5





6 Physics











(A)

+

=

)exp( i

ii

E

gn

βα

(B)

minus+

=

1)exp( i

ii

E

gn

βα

(C)

++

=

1)exp( i

ii

E

gn

βα

(D)

+minus

=

)exp(1 i

ii

E

gn

βα












Physics 7






(D) be zero









(A) [ ]1)exp(

8 3

minus

=

minus

Tkhc

hcE

Bλ

λπ (B)

[ ]1)exp(

8 5

+

=

minus

Tkhc

hcE

Bλ

λπ

(C) [ ]1)exp(

8 3

+

=

minus

Tkhc

hcE

Bλ

λπ (D)

[ ]1)exp(

8 5

minus

=

minus

Tkhc

hcE

Bλ

λπ


acceleration is



(C) 50 ms2 (D) 002 ms2


8 Physics






(A) 5593 Hz (B) 5593 Hz (C) 5593 Hz (D) 5593 Hz








Physics 9













10 Physics



(A) ρ

ε0 (B)

ρ

3ε0

(C) 4πr3

3 ρ

ε0 (D)

rρ

3ε0


(A) nabla rarr


rarr

E = 0

(C) nabla times

rarr

E = ndash part

rarr

B

partt (D) nabla

rarr

E = ρ




2 V = ndash 4πρ


2 V = ndash

ρ

ε0


(A) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J + micro0 ε0 part

rarr

E

partt

(B) nabla rarr

E = 0 nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt

(C) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J

(D) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt


Physics 11



(A) 0Bmicro

1B

micro

1and 0EE0BBσDD ||

22

||1

1

||2


perpperpperpperp

(B) 0B

micro

1B

micro

1and

t

BEE0BB0DD ||

22

||1

1

||2

||12121 =minus

part


perpperpperpperp

(C) 0B

micro

1B

micro


22

||1

1

||2


perpperpperpperp

(D) 0B

micro

1B

micro

1and 0EE0BB0DD ||

22

||1

1

||2


perpperpperpperp




(C) If L 0dlB =


(D) None of these








12 Physics








35 If rarr

n


k


rarr



rarr

n = rarr

k (B) rarr

n = ndash rarr

k

(C) rarr

n rarr

k = 0 (D) rarr

n times rarr

k = 0



Physics 13



(A) Bmicro

1 Eε

00

rr+ (B) B E

micro

ε

0

0rr

sdot

(C) 22

0

0 B E 2micro

εsdot (D)

+

2

0

20 B

micro

1Eε

2

1




















14 Physics











(A) (63 times 10)64 V (B) 1064 V

(C) 10 V (D) 64 V



(A) 3 (B) 1

(C) 0 (D) frac12











Physics 15









16 Physics







(A) 1 (B) 050 (C) 025 (D) 0









Physics 17






L

)sin(2πA)(ψ




)sin(2πA)(ψ








18 Physics




(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20


x+rarr NC14

7

14



x+rarr NC14

7

14














Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


4 Physics










Physics 5





6 Physics











(A)

+

=

)exp( i

ii

E

gn

βα

(B)

minus+

=

1)exp( i

ii

E

gn

βα

(C)

++

=

1)exp( i

ii

E

gn

βα

(D)

+minus

=

)exp(1 i

ii

E

gn

βα












Physics 7






(D) be zero









(A) [ ]1)exp(

8 3

minus

=

minus

Tkhc

hcE

Bλ

λπ (B)

[ ]1)exp(

8 5

+

=

minus

Tkhc

hcE

Bλ

λπ

(C) [ ]1)exp(

8 3

+

=

minus

Tkhc

hcE

Bλ

λπ (D)

[ ]1)exp(

8 5

minus

=

minus

Tkhc

hcE

Bλ

λπ


acceleration is



(C) 50 ms2 (D) 002 ms2


8 Physics






(A) 5593 Hz (B) 5593 Hz (C) 5593 Hz (D) 5593 Hz








Physics 9













10 Physics



(A) ρ

ε0 (B)

ρ

3ε0

(C) 4πr3

3 ρ

ε0 (D)

rρ

3ε0


(A) nabla rarr


rarr

E = 0

(C) nabla times

rarr

E = ndash part

rarr

B

partt (D) nabla

rarr

E = ρ




2 V = ndash 4πρ


2 V = ndash

ρ

ε0


(A) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J + micro0 ε0 part

rarr

E

partt

(B) nabla rarr

E = 0 nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt

(C) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J

(D) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt


Physics 11



(A) 0Bmicro

1B

micro

1and 0EE0BBσDD ||

22

||1

1

||2


perpperpperpperp

(B) 0B

micro

1B

micro

1and

t

BEE0BB0DD ||

22

||1

1

||2

||12121 =minus

part


perpperpperpperp

(C) 0B

micro

1B

micro


22

||1

1

||2


perpperpperpperp

(D) 0B

micro

1B

micro

1and 0EE0BB0DD ||

22

||1

1

||2


perpperpperpperp




(C) If L 0dlB =


(D) None of these








12 Physics








35 If rarr

n


k


rarr



rarr

n = rarr

k (B) rarr

n = ndash rarr

k

(C) rarr

n rarr

k = 0 (D) rarr

n times rarr

k = 0



Physics 13



(A) Bmicro

1 Eε

00

rr+ (B) B E

micro

ε

0

0rr

sdot

(C) 22

0

0 B E 2micro

εsdot (D)

+

2

0

20 B

micro

1Eε

2

1




















14 Physics











(A) (63 times 10)64 V (B) 1064 V

(C) 10 V (D) 64 V



(A) 3 (B) 1

(C) 0 (D) frac12











Physics 15









16 Physics







(A) 1 (B) 050 (C) 025 (D) 0









Physics 17






L

)sin(2πA)(ψ




)sin(2πA)(ψ








18 Physics




(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20


x+rarr NC14

7

14



x+rarr NC14

7

14














Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


Physics 5





6 Physics











(A)

+

=

)exp( i

ii

E

gn

βα

(B)

minus+

=

1)exp( i

ii

E

gn

βα

(C)

++

=

1)exp( i

ii

E

gn

βα

(D)

+minus

=

)exp(1 i

ii

E

gn

βα












Physics 7






(D) be zero









(A) [ ]1)exp(

8 3

minus

=

minus

Tkhc

hcE

Bλ

λπ (B)

[ ]1)exp(

8 5

+

=

minus

Tkhc

hcE

Bλ

λπ

(C) [ ]1)exp(

8 3

+

=

minus

Tkhc

hcE

Bλ

λπ (D)

[ ]1)exp(

8 5

minus

=

minus

Tkhc

hcE

Bλ

λπ


acceleration is



(C) 50 ms2 (D) 002 ms2


8 Physics






(A) 5593 Hz (B) 5593 Hz (C) 5593 Hz (D) 5593 Hz








Physics 9













10 Physics



(A) ρ

ε0 (B)

ρ

3ε0

(C) 4πr3

3 ρ

ε0 (D)

rρ

3ε0


(A) nabla rarr


rarr

E = 0

(C) nabla times

rarr

E = ndash part

rarr

B

partt (D) nabla

rarr

E = ρ




2 V = ndash 4πρ


2 V = ndash

ρ

ε0


(A) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J + micro0 ε0 part

rarr

E

partt

(B) nabla rarr

E = 0 nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt

(C) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J

(D) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt


Physics 11



(A) 0Bmicro

1B

micro

1and 0EE0BBσDD ||

22

||1

1

||2


perpperpperpperp

(B) 0B

micro

1B

micro

1and

t

BEE0BB0DD ||

22

||1

1

||2

||12121 =minus

part


perpperpperpperp

(C) 0B

micro

1B

micro


22

||1

1

||2


perpperpperpperp

(D) 0B

micro

1B

micro

1and 0EE0BB0DD ||

22

||1

1

||2


perpperpperpperp




(C) If L 0dlB =


(D) None of these








12 Physics








35 If rarr

n


k


rarr



rarr

n = rarr

k (B) rarr

n = ndash rarr

k

(C) rarr

n rarr

k = 0 (D) rarr

n times rarr

k = 0



Physics 13



(A) Bmicro

1 Eε

00

rr+ (B) B E

micro

ε

0

0rr

sdot

(C) 22

0

0 B E 2micro

εsdot (D)

+

2

0

20 B

micro

1Eε

2

1




















14 Physics











(A) (63 times 10)64 V (B) 1064 V

(C) 10 V (D) 64 V



(A) 3 (B) 1

(C) 0 (D) frac12











Physics 15









16 Physics







(A) 1 (B) 050 (C) 025 (D) 0









Physics 17






L

)sin(2πA)(ψ




)sin(2πA)(ψ








18 Physics




(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20


x+rarr NC14

7

14



x+rarr NC14

7

14














Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


6 Physics











(A)

+

=

)exp( i

ii

E

gn

βα

(B)

minus+

=

1)exp( i

ii

E

gn

βα

(C)

++

=

1)exp( i

ii

E

gn

βα

(D)

+minus

=

)exp(1 i

ii

E

gn

βα












Physics 7






(D) be zero









(A) [ ]1)exp(

8 3

minus

=

minus

Tkhc

hcE

Bλ

λπ (B)

[ ]1)exp(

8 5

+

=

minus

Tkhc

hcE

Bλ

λπ

(C) [ ]1)exp(

8 3

+

=

minus

Tkhc

hcE

Bλ

λπ (D)

[ ]1)exp(

8 5

minus

=

minus

Tkhc

hcE

Bλ

λπ


acceleration is



(C) 50 ms2 (D) 002 ms2


8 Physics






(A) 5593 Hz (B) 5593 Hz (C) 5593 Hz (D) 5593 Hz








Physics 9













10 Physics



(A) ρ

ε0 (B)

ρ

3ε0

(C) 4πr3

3 ρ

ε0 (D)

rρ

3ε0


(A) nabla rarr


rarr

E = 0

(C) nabla times

rarr

E = ndash part

rarr

B

partt (D) nabla

rarr

E = ρ




2 V = ndash 4πρ


2 V = ndash

ρ

ε0


(A) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J + micro0 ε0 part

rarr

E

partt

(B) nabla rarr

E = 0 nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt

(C) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J

(D) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt


Physics 11



(A) 0Bmicro

1B

micro

1and 0EE0BBσDD ||

22

||1

1

||2


perpperpperpperp

(B) 0B

micro

1B

micro

1and

t

BEE0BB0DD ||

22

||1

1

||2

||12121 =minus

part


perpperpperpperp

(C) 0B

micro

1B

micro


22

||1

1

||2


perpperpperpperp

(D) 0B

micro

1B

micro

1and 0EE0BB0DD ||

22

||1

1

||2


perpperpperpperp




(C) If L 0dlB =


(D) None of these








12 Physics








35 If rarr

n


k


rarr



rarr

n = rarr

k (B) rarr

n = ndash rarr

k

(C) rarr

n rarr

k = 0 (D) rarr

n times rarr

k = 0



Physics 13



(A) Bmicro

1 Eε

00

rr+ (B) B E

micro

ε

0

0rr

sdot

(C) 22

0

0 B E 2micro

εsdot (D)

+

2

0

20 B

micro

1Eε

2

1




















14 Physics











(A) (63 times 10)64 V (B) 1064 V

(C) 10 V (D) 64 V



(A) 3 (B) 1

(C) 0 (D) frac12











Physics 15









16 Physics







(A) 1 (B) 050 (C) 025 (D) 0









Physics 17






L

)sin(2πA)(ψ




)sin(2πA)(ψ








18 Physics




(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20


x+rarr NC14

7

14



x+rarr NC14

7

14














Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


Physics 7






(D) be zero









(A) [ ]1)exp(

8 3

minus

=

minus

Tkhc

hcE

Bλ

λπ (B)

[ ]1)exp(

8 5

+

=

minus

Tkhc

hcE

Bλ

λπ

(C) [ ]1)exp(

8 3

+

=

minus

Tkhc

hcE

Bλ

λπ (D)

[ ]1)exp(

8 5

minus

=

minus

Tkhc

hcE

Bλ

λπ


acceleration is



(C) 50 ms2 (D) 002 ms2


8 Physics






(A) 5593 Hz (B) 5593 Hz (C) 5593 Hz (D) 5593 Hz








Physics 9













10 Physics



(A) ρ

ε0 (B)

ρ

3ε0

(C) 4πr3

3 ρ

ε0 (D)

rρ

3ε0


(A) nabla rarr


rarr

E = 0

(C) nabla times

rarr

E = ndash part

rarr

B

partt (D) nabla

rarr

E = ρ




2 V = ndash 4πρ


2 V = ndash

ρ

ε0


(A) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J + micro0 ε0 part

rarr

E

partt

(B) nabla rarr

E = 0 nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt

(C) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J

(D) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt


Physics 11



(A) 0Bmicro

1B

micro

1and 0EE0BBσDD ||

22

||1

1

||2


perpperpperpperp

(B) 0B

micro

1B

micro

1and

t

BEE0BB0DD ||

22

||1

1

||2

||12121 =minus

part


perpperpperpperp

(C) 0B

micro

1B

micro


22

||1

1

||2


perpperpperpperp

(D) 0B

micro

1B

micro

1and 0EE0BB0DD ||

22

||1

1

||2


perpperpperpperp




(C) If L 0dlB =


(D) None of these








12 Physics








35 If rarr

n


k


rarr



rarr

n = rarr

k (B) rarr

n = ndash rarr

k

(C) rarr

n rarr

k = 0 (D) rarr

n times rarr

k = 0



Physics 13



(A) Bmicro

1 Eε

00

rr+ (B) B E

micro

ε

0

0rr

sdot

(C) 22

0

0 B E 2micro

εsdot (D)

+

2

0

20 B

micro

1Eε

2

1




















14 Physics











(A) (63 times 10)64 V (B) 1064 V

(C) 10 V (D) 64 V



(A) 3 (B) 1

(C) 0 (D) frac12











Physics 15









16 Physics







(A) 1 (B) 050 (C) 025 (D) 0









Physics 17






L

)sin(2πA)(ψ




)sin(2πA)(ψ








18 Physics




(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20


x+rarr NC14

7

14



x+rarr NC14

7

14














Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


8 Physics






(A) 5593 Hz (B) 5593 Hz (C) 5593 Hz (D) 5593 Hz








Physics 9













10 Physics



(A) ρ

ε0 (B)

ρ

3ε0

(C) 4πr3

3 ρ

ε0 (D)

rρ

3ε0


(A) nabla rarr


rarr

E = 0

(C) nabla times

rarr

E = ndash part

rarr

B

partt (D) nabla

rarr

E = ρ




2 V = ndash 4πρ


2 V = ndash

ρ

ε0


(A) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J + micro0 ε0 part

rarr

E

partt

(B) nabla rarr

E = 0 nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt

(C) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J

(D) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt


Physics 11



(A) 0Bmicro

1B

micro

1and 0EE0BBσDD ||

22

||1

1

||2


perpperpperpperp

(B) 0B

micro

1B

micro

1and

t

BEE0BB0DD ||

22

||1

1

||2

||12121 =minus

part


perpperpperpperp

(C) 0B

micro

1B

micro


22

||1

1

||2


perpperpperpperp

(D) 0B

micro

1B

micro

1and 0EE0BB0DD ||

22

||1

1

||2


perpperpperpperp




(C) If L 0dlB =


(D) None of these








12 Physics








35 If rarr

n


k


rarr



rarr

n = rarr

k (B) rarr

n = ndash rarr

k

(C) rarr

n rarr

k = 0 (D) rarr

n times rarr

k = 0



Physics 13



(A) Bmicro

1 Eε

00

rr+ (B) B E

micro

ε

0

0rr

sdot

(C) 22

0

0 B E 2micro

εsdot (D)

+

2

0

20 B

micro

1Eε

2

1




















14 Physics











(A) (63 times 10)64 V (B) 1064 V

(C) 10 V (D) 64 V



(A) 3 (B) 1

(C) 0 (D) frac12











Physics 15









16 Physics







(A) 1 (B) 050 (C) 025 (D) 0









Physics 17






L

)sin(2πA)(ψ




)sin(2πA)(ψ








18 Physics




(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20


x+rarr NC14

7

14



x+rarr NC14

7

14














Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


Physics 9













10 Physics



(A) ρ

ε0 (B)

ρ

3ε0

(C) 4πr3

3 ρ

ε0 (D)

rρ

3ε0


(A) nabla rarr


rarr

E = 0

(C) nabla times

rarr

E = ndash part

rarr

B

partt (D) nabla

rarr

E = ρ




2 V = ndash 4πρ


2 V = ndash

ρ

ε0


(A) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J + micro0 ε0 part

rarr

E

partt

(B) nabla rarr

E = 0 nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt

(C) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J

(D) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt


Physics 11



(A) 0Bmicro

1B

micro

1and 0EE0BBσDD ||

22

||1

1

||2


perpperpperpperp

(B) 0B

micro

1B

micro

1and

t

BEE0BB0DD ||

22

||1

1

||2

||12121 =minus

part


perpperpperpperp

(C) 0B

micro

1B

micro


22

||1

1

||2


perpperpperpperp

(D) 0B

micro

1B

micro

1and 0EE0BB0DD ||

22

||1

1

||2


perpperpperpperp




(C) If L 0dlB =


(D) None of these








12 Physics








35 If rarr

n


k


rarr



rarr

n = rarr

k (B) rarr

n = ndash rarr

k

(C) rarr

n rarr

k = 0 (D) rarr

n times rarr

k = 0



Physics 13



(A) Bmicro

1 Eε

00

rr+ (B) B E

micro

ε

0

0rr

sdot

(C) 22

0

0 B E 2micro

εsdot (D)

+

2

0

20 B

micro

1Eε

2

1




















14 Physics











(A) (63 times 10)64 V (B) 1064 V

(C) 10 V (D) 64 V



(A) 3 (B) 1

(C) 0 (D) frac12











Physics 15









16 Physics







(A) 1 (B) 050 (C) 025 (D) 0









Physics 17






L

)sin(2πA)(ψ




)sin(2πA)(ψ








18 Physics




(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20


x+rarr NC14

7

14



x+rarr NC14

7

14














Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


10 Physics



(A) ρ

ε0 (B)

ρ

3ε0

(C) 4πr3

3 ρ

ε0 (D)

rρ

3ε0


(A) nabla rarr


rarr

E = 0

(C) nabla times

rarr

E = ndash part

rarr

B

partt (D) nabla

rarr

E = ρ




2 V = ndash 4πρ


2 V = ndash

ρ

ε0


(A) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J + micro0 ε0 part

rarr

E

partt

(B) nabla rarr

E = 0 nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt

(C) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0

rarr

J

(D) nabla rarr

E = ρ nabla rarr

B = 0 nabla times

rarr

E = ndash part

rarr

B

partt nabla times

rarr

B = micro0 ε0 part

rarr

E

partt


Physics 11



(A) 0Bmicro

1B

micro

1and 0EE0BBσDD ||

22

||1

1

||2


perpperpperpperp

(B) 0B

micro

1B

micro

1and

t

BEE0BB0DD ||

22

||1

1

||2

||12121 =minus

part


perpperpperpperp

(C) 0B

micro

1B

micro


22

||1

1

||2


perpperpperpperp

(D) 0B

micro

1B

micro

1and 0EE0BB0DD ||

22

||1

1

||2


perpperpperpperp




(C) If L 0dlB =


(D) None of these








12 Physics








35 If rarr

n


k


rarr



rarr

n = rarr

k (B) rarr

n = ndash rarr

k

(C) rarr

n rarr

k = 0 (D) rarr

n times rarr

k = 0



Physics 13



(A) Bmicro

1 Eε

00

rr+ (B) B E

micro

ε

0

0rr

sdot

(C) 22

0

0 B E 2micro

εsdot (D)

+

2

0

20 B

micro

1Eε

2

1




















14 Physics











(A) (63 times 10)64 V (B) 1064 V

(C) 10 V (D) 64 V



(A) 3 (B) 1

(C) 0 (D) frac12











Physics 15









16 Physics







(A) 1 (B) 050 (C) 025 (D) 0









Physics 17






L

)sin(2πA)(ψ




)sin(2πA)(ψ








18 Physics




(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20


x+rarr NC14

7

14



x+rarr NC14

7

14














Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


Physics 11



(A) 0Bmicro

1B

micro

1and 0EE0BBσDD ||

22

||1

1

||2


perpperpperpperp

(B) 0B

micro

1B

micro

1and

t

BEE0BB0DD ||

22

||1

1

||2

||12121 =minus

part


perpperpperpperp

(C) 0B

micro

1B

micro


22

||1

1

||2


perpperpperpperp

(D) 0B

micro

1B

micro

1and 0EE0BB0DD ||

22

||1

1

||2


perpperpperpperp




(C) If L 0dlB =


(D) None of these








12 Physics








35 If rarr

n


k


rarr



rarr

n = rarr

k (B) rarr

n = ndash rarr

k

(C) rarr

n rarr

k = 0 (D) rarr

n times rarr

k = 0



Physics 13



(A) Bmicro

1 Eε

00

rr+ (B) B E

micro

ε

0

0rr

sdot

(C) 22

0

0 B E 2micro

εsdot (D)

+

2

0

20 B

micro

1Eε

2

1




















14 Physics











(A) (63 times 10)64 V (B) 1064 V

(C) 10 V (D) 64 V



(A) 3 (B) 1

(C) 0 (D) frac12











Physics 15









16 Physics







(A) 1 (B) 050 (C) 025 (D) 0









Physics 17






L

)sin(2πA)(ψ




)sin(2πA)(ψ








18 Physics




(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20


x+rarr NC14

7

14



x+rarr NC14

7

14














Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


12 Physics








35 If rarr

n


k


rarr



rarr

n = rarr

k (B) rarr

n = ndash rarr

k

(C) rarr

n rarr

k = 0 (D) rarr

n times rarr

k = 0



Physics 13



(A) Bmicro

1 Eε

00

rr+ (B) B E

micro

ε

0

0rr

sdot

(C) 22

0

0 B E 2micro

εsdot (D)

+

2

0

20 B

micro

1Eε

2

1




















14 Physics











(A) (63 times 10)64 V (B) 1064 V

(C) 10 V (D) 64 V



(A) 3 (B) 1

(C) 0 (D) frac12











Physics 15









16 Physics







(A) 1 (B) 050 (C) 025 (D) 0









Physics 17






L

)sin(2πA)(ψ




)sin(2πA)(ψ








18 Physics




(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20


x+rarr NC14

7

14



x+rarr NC14

7

14














Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


Physics 13



(A) Bmicro

1 Eε

00

rr+ (B) B E

micro

ε

0

0rr

sdot

(C) 22

0

0 B E 2micro

εsdot (D)

+

2

0

20 B

micro

1Eε

2

1




















14 Physics











(A) (63 times 10)64 V (B) 1064 V

(C) 10 V (D) 64 V



(A) 3 (B) 1

(C) 0 (D) frac12











Physics 15









16 Physics







(A) 1 (B) 050 (C) 025 (D) 0









Physics 17






L

)sin(2πA)(ψ




)sin(2πA)(ψ








18 Physics




(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20


x+rarr NC14

7

14



x+rarr NC14

7

14














Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


14 Physics











(A) (63 times 10)64 V (B) 1064 V

(C) 10 V (D) 64 V



(A) 3 (B) 1

(C) 0 (D) frac12











Physics 15









16 Physics







(A) 1 (B) 050 (C) 025 (D) 0









Physics 17






L

)sin(2πA)(ψ




)sin(2πA)(ψ








18 Physics




(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20


x+rarr NC14

7

14



x+rarr NC14

7

14














Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


Physics 15









16 Physics







(A) 1 (B) 050 (C) 025 (D) 0









Physics 17






L

)sin(2πA)(ψ




)sin(2πA)(ψ








18 Physics




(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20


x+rarr NC14

7

14



x+rarr NC14

7

14














Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


16 Physics







(A) 1 (B) 050 (C) 025 (D) 0









Physics 17






L

)sin(2πA)(ψ




)sin(2πA)(ψ








18 Physics




(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20


x+rarr NC14

7

14



x+rarr NC14

7

14














Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


Physics 17






L

)sin(2πA)(ψ




)sin(2πA)(ψ








18 Physics




(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20


x+rarr NC14

7

14



x+rarr NC14

7

14














Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


18 Physics




(A) l(l + 1) ħ2

2mr20

(B) l2 ħ2

2mr20

(C) l(l + 1) ħ2

mr20

(D) l2 ħ2

mr20


x+rarr NC14

7

14



x+rarr NC14

7

14














Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


Physics 19




20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


20 Physics




























Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


Physics 21













(A) U238 (B) Fe56

(C) Ag107 (D) Pb206









(A) (231) (B) (132)

(C) (326) (D) (123)


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


22 Physics









(A) 50 eV (B) 62 eV

(C) 67 eV (D) 70 eV










Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


Physics 23



















(A) ħ2

dK

dt (B) ħ2

d2K

dt2

(C) ħ

dK

dt (D) ħ

d2K

dt2


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


24 Physics

















k

E 1

2

k

E 1

2


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


Physics 25








(A) 4505 MHz (B) 4752 MHz













26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


26 Physics











Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


Physics 27


(A) π

24 (B)

π

12

(C) π

6 (D)

π

60










28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


28 Physics



dyx

dx

ydx log2

2

22

=+minus is

where Zex =


dyx

dx

ydx log2

2

22





minus )( 21


2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx

yd is


0)1(1

2

2

2

2

=minus+

+ y

x

n

dx

dy

xdx




Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


Physics 29


=12

1

n n is


=12

1



(A) 6

π (B)

6

2π

(C) 6

3π

(D) 6

4π











____________


30 Physics



Physics 31























GFGC


30 Physics



Physics 31























GFGC


Physics 31























GFGC






















GFGC

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